Variance-Weighted Regression Trend [BackQuant]Variance-Weighted Regression Trend
Overview
Variance-Weighted Regression Trend is a rolling linear-regression trend indicator that adjusts the influence of observations according to the estimated variance of their regression residuals.
The script first calculates a standard ordinary least-squares regression across the selected window. It then measures the squared residuals around that fit and uses those residuals to estimate how variable the regression error has been through the sample.
Those variance estimates are converted into relative weights. Lower estimated residual variance can receive more influence, while higher estimated residual variance can receive less. A second weighted regression is then calculated using those weights.
The indicator also includes:
EMA, RMA or rolling-average residual variance.
Configurable inverse-variance weighting strength.
Weight regularization and upper/lower weight limits.
Weighted R² and slope-quality diagnostics.
Two regression-channel methods.
Optional trend-flip quality confirmation.
OLS comparison.
Linear regression projection.
Trend colouring and alerts.
Calculation
The basic process is:
Fit an ordinary least-squares regression over the Regression Length.
Calculate the squared residual of every observation around that fit.
Smooth those squared residuals to estimate local residual variance.
Add a regularization floor to reduce unstable extreme weights.
Convert variance into relative observation weights.
Clamp weights between the selected minimum and maximum.
Calculate a second weighted regression.
The weighted line is therefore influenced more by observations receiving larger relative weights and less by those receiving smaller ones.
Variance Weighting
The weighting is based on regression residual variance , not ATR, trading volume or raw price volatility.
For each point:
Residual = Source - OLS fitted value
Squared Residual = Residual²
The squared residuals are then processed using the selected Variance Model.
EMA
Uses exponential smoothing and responds more quickly to recent residual changes.
RMA
Uses a slower recursive smoothing process.
Rolling Mean
Uses a finite moving average of squared residuals.
Weight Power
Weight Power controls how strongly estimated variance affects the regression.
The raw weighting relationship is:
Weight ∝ 1 / Variance^Weight Power
0 gives equal weighting, making the final fit behave like the OLS regression.
1 applies standard inverse-variance-style weighting.
Values above 1 increase the difference between low- and high-variance observations.
Higher settings can make the regression more selective, but can also concentrate too much influence in a small part of the sample.
Variance Regularization
Very small variance estimates can otherwise create extremely large inverse weights.
The script therefore adds a fraction of the window's mean squared residual to each local variance estimate.
Higher regularization makes the weights more uniform.
Lower regularization allows stronger differences between observations.
Minimum and Maximum Relative Weight
Raw weights are normalized relative to their average before being clamped.
A relative weight above 1 means the observation has greater-than-average influence.
A value below 1 means it has less.
The Minimum Relative Weight prevents high-variance observations from effectively disappearing from the regression.
The Maximum Relative Weight prevents very low-variance observations from dominating the entire fit.
Weighted Regression
Once the final weights are calculated, the script solves a weighted linear regression:
Y = Intercept + Slope × X
The displayed line is the current endpoint of that rolling weighted regression.
Each new bar shifts the regression window and recalculates:
OLS.
Residuals.
Variance estimates.
Weights.
Weighted slope and intercept.
OLS Comparison
The optional OLS line shows the endpoint of the initial equal-weight regression.
This makes it easy to see how much the variance weighting is actually changing the result.
If Weight Power is set to 0, the weighted regression and OLS should be effectively aligned.
As the weighting becomes more aggressive, the lines may separate depending on the residual structure inside the window.
Trend State
Trend direction comes from the sign of the weighted regression slope.
Positive slope = bullish.
Negative slope = bearish.
A bullish flip occurs when the stored trend changes from bearish to bullish.
A bearish flip occurs when it changes from bullish to bearish.
Quality Confirmation
Quality Confirmation can be enabled to prevent weak slope changes from immediately flipping the trend state.
When enabled, an opposite slope must also satisfy:
Minimum Weighted R².
Minimum Slope / Standard Error.
If those conditions are not met, the existing trend state remains active even if the current slope temporarily changes sign.
Weighted R²
Weighted R² measures how well the weighted straight-line regression describes the current sample.
Higher values indicate that the weighted observations are more closely aligned with a linear fit.
Lower values indicate a less orderly linear relationship.
R² does not determine trend direction and should not be interpreted as a forecast of future performance.
Slope / Standard Error
The script calculates the absolute weighted slope relative to its estimated standard error:
|Slope| / Slope Standard Error
This is used as a practical slope-quality measure.
Higher values indicate that the fitted slope is larger relative to the estimated regression error.
It is used by the optional Quality Confirmation setting and is not presented as a formal significance test.
Regression Channels
Two channel-width methods are available.
Weighted Residual RMS
Uses the weighted root-mean-square distance of observations from the fitted regression.
This reflects the general amount of scatter around the line.
Regression Standard Error
Uses the calculated standard error of the fitted current regression value.
This normally represents a different and often narrower measure than residual RMS.
The Channel Multiplier scales whichever method is selected.
Expand During Poor Fit
When enabled, the channel becomes wider as Weighted R² decreases.
This is intended to visually reflect greater uncertainty when the current window is poorly described by a straight line.
The expansion affects only the channel width.
It does not alter the regression or trend calculation.
Projection
The Projection extends the current regression slope forward by the selected number of bars.
It is simply:
Current fitted line extended using the current slope.
It is not a separate forecasting model.
As the regression changes on new bars, the projection also changes.
Current Relative Weight
The Data Window shows the final relative weight assigned to the newest observation.
A value:
Above 1 = greater-than-average influence.
Below 1 = less-than-average influence.
This can help show how the current observation is being treated by the variance-weighting model.
Effective Sample Size
The indicator also reports:
Effective N = (Sum of Weights)² / Sum of Squared Weights
This provides a simple measure of weight concentration.
If weights are similar, Effective N remains close to the full Regression Length.
If a smaller group of observations receives most of the weight, Effective N falls.
This is useful when experimenting with aggressive Weight Power or wide weight limits.
Trend Strength
Trend Strength is used only for the regression glow.
It combines:
60% Weighted R².
40% normalized Slope / Standard Error.
It does not affect the regression or signals.
ATR(14) is used only to scale the visual width of the glow and flip bloom to the instrument.
Input Guide
Regression Length
Controls the size of the rolling regression sample.
Projection Bars
Controls how far the current fitted slope is extended visually.
Variance Length
Controls how quickly the residual-variance estimate changes.
Variance Model
Selects EMA, RMA or Rolling Mean smoothing of squared residuals.
Weight Power
Controls the strength of inverse-variance weighting.
Variance Regularization
Reduces extreme differences between weights.
Minimum / Maximum Relative Weight
Limits how little or how much influence any one observation can receive.
Channel Width
Selects Weighted Residual RMS or Regression Standard Error.
Channel Multiplier
Scales the regression channel.
Poor Fit Expansion
Optionally widens the channel as R² deteriorates.
Quality Confirmation
Requires minimum regression fit and slope quality before allowing trend flips.
How to use it
The indicator can be used as:
A regression-based trend filter.
A comparison between ordinary and variance-weighted regression.
A way to study how residual-based weighting changes a rolling trend estimate.
A trend-quality filter using R² and slope strength.
A regression channel for visualizing fit dispersion.
The OLS Comparison and Data Window values are particularly useful when testing the weighting settings, because they show whether the extra weighting is materially changing the regression or simply producing a result close to ordinary least squares.
Limitations
The variance estimates are derived from OLS residuals inside the same rolling window.
The model is a custom two-stage weighted regression rather than a full generalized least-squares procedure.
Higher Weight Power can concentrate the fit in a relatively small part of the sample.
Linear regression cannot represent every type of market structure.
High R² does not imply future trend continuation.
The forward projection is only a linear extrapolation of the current fit.
Quality Confirmation can reduce weak flips but can also delay genuine changes in direction.
Data Window
The script exposes:
Weighted Slope.
Weighted R².
Slope / Standard Error.
Weighted Residual RMS.
Regression Standard Error.
Current Relative Weight.
Effective Sample Size.
Trend Strength.
Alerts
The indicator includes:
Variance-Weighted Regression Bullish: trend changes from bearish to bullish.
Variance-Weighted Regression Bearish: trend changes from bullish to bearish.
Variance-Weighted Regression Flip: either transition occurs.
Summary
Variance-Weighted Regression Trend starts with a normal rolling OLS regression, measures the residual variance around that fit, and uses those estimates to assign relative weights to the observations in a second regression.
The weighting strength, variance smoothing, regularization and weight limits are all configurable, making it possible to move from essentially equal-weight OLS to a much more selective fit.
The final weighted slope controls the trend state, while Weighted R² and the Slope / Standard Error score can optionally be used to filter weak reversals.
Regression channels, OLS comparison, forward projection and the visual strength system provide additional context around the core weighted regression without changing the underlying trend logic.
Indicador
Pattern Atlas : Geometric [AxeAlgo]Pattern Atlas : Geometric Patterns
WHAT THIS LIBRARY IS
This is a Pine Script v6 library of 17 classical chart pattern detectors — Head and Shoulders, Double/Triple Tops and Bottoms, triangles, wedges, flags, and the rest of the standard technical-analysis catalog built from swing highs and lows rather than single-candle shape. Unlike candlestick patterns, which read one to a handful of fixed bars, chart patterns span a variable, often large number of bars, so this library carries one small piece of state — a rolling history of confirmed swing pivots — that every pattern function reads from. Beyond that, the same philosophy as Library #1 applies: no plotting, no alerts, and no inputs in this script by design, since a library's job is to hand other scripts a clean, reusable, well-documented API, not to draw on a chart itself (Pine doesn't allow a library to plot anything anyway). If you're looking for a ready-to-use indicator built on top of this library, see the companion "Pattern Atlas : Geometric Indicator " script, which imports every function here and turns it into on-chart signals, measured-move price targets, a live scanner table, and alerts.
Chart pattern analysis is one of the foundational tools of classical technical analysis, going back to Edwards and Magee's original work and refined since by researchers like Thomas Bulkowski, whose statistical studies of pattern behavior are the closest thing this field has to an industry-standard reference. The patterns in this library follow that standard catalog, so anyone who already knows what a Head and Shoulders top or an Ascending Triangle looks like will recognize exactly what each function is checking for.
WHY A LIBRARY INSTEAD OF ONE MONOLITHIC INDICATOR
Splitting detection logic out as an importable library means:
- Any Pine coder building their own strategy, indicator, or screener can pull in exactly the pattern checks they need without copy-pasting swing-pivot and trendline math into every new script.
- The detection logic is tested and maintained in one place. When a threshold gets refined, everything importing this library benefits from the update by bumping one version number.
- It keeps the math separate from presentation — how a pattern gets drawn, colored, or alerted on is a completely separate decision from whether the pattern is actually present, and different users want different presentations.
HOW TO IMPORT AND USE IT
Add this line near the top of your script (adjust the version number to whatever the current published version is):
import AxeAlgo/Pattern_Atlas_Geometric/1 as geo
Unlike Library #1, most of the functions here need a shared pivot history to work from. Call trackPivots() exactly once per bar, then pass its result into every detect*() function that needs it:
pivots = geo.trackPivots()
match = geo.detectDoubleTopBottom(pivots)
if match.found
label.new(bar_index, high, match.patternName)
Four functions — detectSpike(), detectFlag(), detectPennant(), and detectIslandReversal() — read directly off recent price action instead of the shared pivot history, so they're called without a pivots argument: geo.detectSpike().
trackPivots() takes three optional parameters: leftBars and rightBars (how many less-extreme bars must surround a candidate swing point before it confirms as a pivot — higher values mean fewer, more significant pivots, at the cost of a longer confirmation lag), and maxPivots (how much pivot history to retain). All three have sensible defaults.
Every detect*() function returns the same structure, called ChartPatternMatch, so the calling pattern is identical no matter which of the 17 you use. It has nine fields:
- found — true if the pattern matched at the evaluated bar, false otherwise.
- patternName — the specific name of what matched (e.g. "Ascending Triangle"), na when not found.
- direction — "bullish" or "bearish".
- pivotBars — bar_index of each pivot the match was built from, in chronological order.
- pivotPrices — price of each pivot, in the same order as pivotBars.
- breakoutLevel — the support, resistance, or neckline level price broke through to confirm the pattern.
- necklineSlope — slope (price per bar) of the breakout line, na when the pattern's breakout level isn't a sloped line.
- barIndex — the bar_index the pattern completes (breaks out) on.
- description — a full sentence naming the pattern and the actual measured price levels that triggered it — genuinely useful for a tooltip or an alert message, not just a repeat of the pattern name.
Two additional exported functions turn that raw match into something more actionable, and both work on any ChartPatternMatch regardless of which detect*() function produced it:
- patternStrength(match) — a 0-100 score for how decisively the confirmation close broke through breakoutLevel, relative to the pattern's own price range. A breakout that clears the level by a meaningful fraction of the pattern's own size scores higher than a one-tick poke through it.
- patternTarget(match) — a classical measured-move price target, projecting the pattern's own height from the breakout point. Returns na for patterns without a reliable height to project from (V-Top/V-Bottom Spike, Island Reversal, Bump-and-Run Reversal).
Every detect*() function also exposes its own set of tunable threshold parameters — how flat a "flat top" has to be, how much two shoulders can differ and still count as equal, and so on — all with sensible defaults so you don't have to touch them unless you want to tighten or loosen a specific pattern's sensitivity for a particular instrument or timeframe.
THE 17 PATTERNS
Reversal patterns (7) — signal a potential change in the prevailing trend:
- Head and Shoulders / Inverse Head and Shoulders — detectHeadAndShoulders(). Three swing extremes with the middle one more extreme than the two roughly-equal outer ones, confirmed when price breaks the neckline connecting the two points between them.
- Double Top / Double Bottom — detectDoubleTopBottom(). Two roughly equal peaks (or troughs) with a retracement between them, confirmed when price breaks back through that retracement level.
- Triple Top / Triple Bottom — detectTripleTopBottom(). The same idea as a Double Top/Bottom with a third roughly-equal touch, confirmed on the break of the support or resistance formed between the touches.
- Rounding Top / Rounding Bottom — detectRoundingTopBottom(). A gradual, curved advance-and-rollover (or decline-and-recovery) between two similar edge levels. Approximate: read from three swing pivots rather than fitting a true curve.
- Diamond Top / Diamond Bottom — detectDiamondTopBottom(). Swing range that widens and then narrows again, confirmed on a break of the resulting support or resistance. Rare and approximate: read from three pivot pairs rather than a clean diamond outline.
- Broadening Formation — detectBroadeningTopBottom(). Diverging highs and lows forming an increasingly volatile range, confirmed on a break of either edge. Approximate: read from two pivot pairs rather than a hand-fitted diverging channel.
- V-Top / V-Bottom (Spike) — detectSpike(). A single sharp extreme with no rounding — a large move into the pivot and an equally large move away from it, both measured against the recent average bar range, within a handful of bars. Self-contained, no pivots argument needed.
Continuation patterns (8) — typically resolve in the direction of the move that preceded them:
- Ascending Triangle — detectTriangleAscending(). Flat resistance with rising support, confirmed on a break above resistance.
- Descending Triangle — detectTriangleDescending(). Flat support with falling resistance, confirmed on a break below support.
- Symmetrical Triangle — detectTriangleSymmetrical(). Converging highs and rising lows, confirmed (bullish or bearish) whichever side the price actually breaks.
- Rising Wedge / Falling Wedge — detectWedge(). Both trendlines slope the same direction and converge; breaks the opposite way from the slope, since the shared-direction move was already losing momentum.
- Bull Flag / Bear Flag — detectFlag(). A strong directional move (the pole), followed by a tight, roughly parallel pullback, confirmed on a break back out in the pole's direction. Self-contained, no pivots argument needed.
- Bull Pennant / Bear Pennant — detectPennant(). The same pole-and-consolidation structure as a Flag, but the consolidation narrows and converges rather than staying parallel. Self-contained, no pivots argument needed.
- Rectangle — detectRectangle(). Price boxed between flat support and flat resistance, confirmed on a break of either edge.
- Cup and Handle / Inverted Cup and Handle — detectCupAndHandle(). A rounded recovery (or decline) back to its starting rim, then a shallow pullback (the handle), confirmed on a break through the rim.
Structural / gap-based patterns (2):
- Bullish / Bearish Island Reversal — detectIslandReversal(). A bar (or small cluster) isolated by a gap on both sides, then abandoned by a gap the other way — an abrupt reversal. Self-contained, pure gap logic, no pivots argument needed.
- Bump-and-Run Reversal — detectBumpAndRun(). A lead-in trendline, then a "bump" phase accelerating well beyond it, then a "run" breaking back through the lead-in line. Approximate: the lead-in line is read from just two pivots rather than a hand-drawn trendline.
WHAT THIS LIBRARY DELIBERATELY DOES NOT DO
No plotting, no drawing, no alertcondition() calls, and no inputs — Pine doesn't allow any of those inside a library in the first place, since a library can never be added to a chart on its own. If you want signals, price targets, a scanner table, or alerts, import this library into your own script (or use the companion "Pattern Atlas : Chart Pattern Scanner " indicator, which does exactly that) rather than expecting this script to render anything by itself.
This library also does not evaluate multi-timeframe data, volume, or broader market structure — it's swing-pivot and trendline geometry only, on purpose, so its behavior is easy to reason about and easy to reuse as one building block among several.
Four of the seventeen patterns are explicitly noted above as approximate: Rounding Top/Bottom, Diamond Top/Bottom, Broadening Formation, and Bump-and-Run Reversal are read from a small, fixed number of swing pivots rather than fitting a true curve or hand-drawn trendline to the data. They will not catch every textbook-perfect example of these shapes, and they may occasionally flag a looser approximation of one. Treat them as a starting point for further chart review, not a final word.
PART OF A LARGER SERIES
This is Library #2 in the AxeAlgo Pattern Atlas — a planned set of Pine libraries splitting pattern detection by the method actually used to find each kind of pattern: candlestick shape (Library #1, already published), classical chart/geometric patterns (this library), harmonic patterns (Fibonacci-ratio XABCD structures), and market-structure concepts (order blocks, liquidity, Wyckoff-style events). Each library is independent and useful on its own; together they're meant to cover technical pattern analysis without forcing unrelated detection methods into the same function.
A NOTE ON REPAINTING
trackPivots() only confirms a swing pivot once rightBars bars have passed since it happened — the same confirmation lag ta.pivothigh()/ta.pivotlow() use, just written out as plain comparisons so it works safely inside a library's exported functions. That means a pivot never moves or disappears once confirmed; it just takes rightBars bars to become known, which is a normal and unavoidable part of swing-pivot detection, not a defect in this library. On the currently-forming bar, a pattern's found status can still change tick to tick as that bar's own high, low, and close move — that's inherent to reading live price action. If you're building persisted signals, drawings, alerts, or price targets on top of these functions (rather than a live "what's happening right now" readout), gate your usage on barstate.isconfirmed so a signal only fires once the bar it describes has actually closed, exactly like the companion scanner indicator does.
DISCLAIMER
This library is a technical analysis tool for identifying classical chart pattern shapes in historical and live price data. It does not predict future price movement, and a detected pattern — including any projected price target — is a description of past price action, not a signal guaranteed to repeat. Nothing in this script constitutes financial advice. Always combine pattern recognition with your own risk management and broader analysis before making any trading decision.
Biblioteca
MAD Volatility Trail [BackQuant]MAD Volatility Trail
Overview
MAD Volatility Trail is a robust trend-following overlay built from a rolling median and Median Absolute Deviation rather than a conventional moving average and standard deviation.
The indicator estimates a central price using the rolling median, measures how widely recent prices are distributed around that median using MAD, converts that dispersion into adaptive upper and lower bands, and then transforms those bands into one-sided trailing boundaries.
The result is a persistent bullish or bearish trend regime with:
A robust median-based center.
MAD-derived volatility bands.
Optional ATR minimum band width.
One-sided trailing support and resistance.
Optional median-slope confirmation.
Bullish and bearish regime flips.
Strength-reactive gradient and glow.
Post-flip bloom visualization.
Trend-coloured candles.
Signal and alert support.
The main distinction is statistical.
Most volatility trails rely on:
Means.
Standard deviation.
ATR.
MAD Volatility Trail instead uses:
Median.
Median Absolute Deviation.
Median-based statistics are substantially less sensitive to isolated extreme observations, making the framework useful when the user wants a trend structure that is less influenced by individual spikes or outliers.
Core concept
The indicator separates the problem into four stages:
Estimate a robust rolling center using the median.
Measure robust dispersion around that center using MAD.
Build upper and lower adaptive deviation bands.
Convert those raw bands into persistent trailing trend boundaries.
The resulting trail behaves conceptually like a volatility-aware regime filter, but its volatility estimate comes primarily from the empirical distribution of price around its median.
Why median instead of mean?
A conventional arithmetic mean is calculated by summing all observations and dividing by their count.
Every value directly affects the result.
This makes the mean sensitive to outliers.
Consider a simplified sample:
100
101
101
102
150
The extreme value at 150 pulls the arithmetic mean upward substantially.
The median is simply the middle observation after sorting:
Median = 101
The single extreme observation has much less influence.
This property is called robustness .
In markets, isolated large candles, gaps, liquidation events and temporary price spikes can distort mean-based statistics. Median-based calculations intentionally reduce the influence of those individual observations.
Rolling median
For each bar, the indicator collects the selected Source values across the MAD Lookback.
It then calculates the exact median of the available observations.
For an odd number of observations, the median is the middle sorted value.
For an even number, the median lies between the two central observations according to the median implementation.
The resulting value becomes the statistical center of the trail.
Unlike an EMA or RMA, the median is not recursively smoothed.
It is recomputed from the actual distribution of values inside the current rolling window.
Early-history behaviour
At the beginning of the chart, the script ignores unavailable historical values.
This means the first valid median calculations may use fewer observations than the full MAD Lookback until sufficient chart history has accumulated.
Once the complete lookback is available, the calculation uses the full selected window.
Median Absolute Deviation
After calculating the rolling median, the script measures the absolute distance of every observation from that median:
Absolute Deviation = |Value - Median|
It then takes the median of those absolute deviations:
MAD = Median(|Xi - Median(X)|)
This is the Median Absolute Deviation .
MAD measures the typical distance of observations from the median.
It serves a role similar to standard deviation, but the mathematics and statistical behaviour are different.
Why MAD is robust
Standard deviation squares deviations from the mean.
Large deviations therefore receive disproportionately large influence.
A single extreme observation can:
Move the mean.
Create a very large squared deviation.
Increase the final standard deviation substantially.
MAD does not square deviations.
It calculates absolute distance and then takes another median.
Extreme values therefore have limited ability to change the result unless enough of the underlying sample shifts.
This gives MAD a high resistance to outliers.
In practical chart terms, one unusual wick or shock candle is less likely to inflate the statistical width as dramatically as it could under a standard-deviation model.
MAD versus standard deviation
The two measures answer related but different questions.
Standard deviation
Measures squared dispersion around the arithmetic mean.
MAD
Measures median absolute dispersion around the median.
Standard deviation is highly useful when a mean-and-variance framework is desired.
MAD is useful when robustness to unusual observations is more important.
The indicator does not claim one is universally superior.
It intentionally uses MAD because the purpose is to construct a robust trend boundary.
MAD Scale
Raw MAD is not numerically identical to standard deviation.
Under a normal distribution, MAD is usually multiplied by a consistency factor of approximately 1.4826 when the goal is to make it comparable to standard deviation.
The indicator exposes this scaling directly:
Robust Deviation = Raw MAD × MAD Scale
The script default is 1.4655.
The input remains fully adjustable, so users who want the conventional normal-consistency approximation can set the factor near 1.4826.
This scale does not change the median itself.
It changes only the size of the deviation estimate used to build the bands.
Deviation Factor
After scaling MAD, the indicator applies the Deviation Factor:
MAD Width = Scaled MAD × Deviation Factor
This acts as the main sensitivity control.
Lower values:
Create narrower raw bands.
Place the trail closer to price.
Produce more frequent regime changes.
Higher values:
Create wider bands.
Require larger movement for reversals.
Produce more persistent trend states.
The MAD Scale and Deviation Factor both affect width, but they represent different concepts.
MAD Scale calibrates the statistical dispersion estimate.
Deviation Factor determines how much of that estimated dispersion is used for the trend envelope.
Raw MAD bands
The raw bands are:
Upper MAD Band = Median + Band Width
Lower MAD Band = Median - Band Width
Before trailing logic is applied, these bands can move freely upward or downward with:
The rolling median.
MAD dispersion.
Any active ATR floor.
These are statistical envelopes around the median.
They are not yet the final trend trail.
ATR Minimum Width
MAD can become extremely small when recent prices are tightly clustered.
In very low-dispersion conditions, this may place the raw bands extremely close to the median.
That can create excessive sensitivity to minor price fluctuations.
The optional ATR Minimum Width provides a secondary floor.
The script calculates:
ATR Floor = ATR(ATR Length) × ATR Floor Multiplier
When enabled:
Band Width = max(MAD Width, ATR Floor)
This means MAD remains the primary volatility model, but the bands cannot contract below the selected ATR-based threshold.
Why use an ATR floor?
MAD and ATR measure different aspects of market behaviour.
MAD measures:
Dispersion of the selected source around its rolling median.
ATR measures:
Bar-to-bar trading range.
Gaps relative to the previous close.
A market can have:
Low median dispersion.
But still produce meaningful intrabar range.
The ATR floor can prevent the trail from becoming unrealistically tight under those conditions.
ATR floor disabled
With ATR Minimum Width disabled, the entire structural width comes from:
MAD × MAD Scale × Deviation Factor
This produces the purest MAD-based version of the indicator.
ATR Length
ATR Length controls the volatility horizon used only for the optional minimum-width calculation.
It does not affect:
The rolling median.
Raw MAD.
Scaled MAD.
Note that the visual glow and bloom later in the script use a fixed ATR(14), separate from this ATR Length input.
Trailing bands
The raw MAD bands are converted into one-sided trails.
This is the stage that turns a statistical envelope into a persistent trend system.
Two independent trails are maintained:
Lower Trail.
Upper Trail.
Lower Trail
When the previous trigger remains above the previous Lower Trail, the new Lower Trail is:
max(Current Raw Lower Band, Previous Lower Trail)
This means the Lower Trail can:
Move upward.
Remain unchanged.
But cannot move downward while the condition remains active.
This creates a ratcheting support structure.
If the trigger falls below the prior Lower Trail, the trail is allowed to reset to the new raw lower band.
Upper Trail
When the previous trigger remains below the previous Upper Trail, the new Upper Trail is:
min(Current Raw Upper Band, Previous Upper Trail)
This means the Upper Trail can:
Move downward.
Remain unchanged.
But cannot move upward while the condition remains active.
This creates a ratcheting resistance structure.
If the trigger rises above the previous Upper Trail, the band can reset to the current raw upper value.
Why trailing the bands matters
A raw median-deviation envelope moves in both directions.
If those raw bands were used directly for trend changes:
The threshold itself could retreat toward price.
Small changes in median or MAD could produce unstable reversals.
The one-sided trail introduces hysteresis .
Hysteresis means that once a trend regime is established, the threshold required to reverse it remains on the opposing side.
This reduces the tendency to flip repeatedly around the rolling median.
Flip Trigger
The user can choose which series is used when evaluating trail breaks:
Close.
Source.
Close
Uses the candle close regardless of which series is used for the MAD calculation.
This is the conventional option.
Source
Uses the selected Source input.
For example, if HLC3 is selected as the Source:
The median is calculated from HLC3.
MAD is calculated from HLC3.
The trail can also be triggered by HLC3.
This keeps the center, dispersion and reversal trigger based on the same source.
Initial trend state
The trend begins in a neutral state.
Once a valid rolling median is available:
Trigger at or above Median = bullish initialization.
Trigger below Median = bearish initialization.
This initial assignment is not treated as a bullish or bearish flip.
Flip signals occur only after the indicator has already established one regime and later transitions into the opposite regime.
Bullish flip
A bullish regime change requires:
Trigger to move above the Upper Trail.
Current trend not already bullish.
Optional bullish median-slope confirmation to pass.
Once confirmed:
Trend becomes bullish.
The Lower Trail becomes the active trend boundary.
A bullish signal can be displayed.
Bearish flip
A bearish regime change requires:
Trigger to move below the Lower Trail.
Current trend not already bearish.
Optional bearish median-slope confirmation to pass.
Once confirmed:
Trend becomes bearish.
The Upper Trail becomes the active boundary.
A bearish signal can be displayed.
Active trend trail
The final displayed trend boundary depends on the regime:
Bullish = Lower Trail.
Bearish = Upper Trail.
This means the line automatically moves to the opposite side of price when a complete regime change occurs.
Median Slope Confirmation
The optional Median Slope Confirmation adds a directional requirement to trend reversals.
For a bullish flip:
Current Median > Median from Slope Lookback bars ago
For a bearish flip:
Current Median < Median from Slope Lookback bars ago
This requires the robust statistical center itself to move in the direction of the proposed new trend.
Why confirm with median slope?
Price can briefly cross a trail while the underlying median remains flat or continues moving in the opposite direction.
Slope confirmation can reject some of these events.
For example:
A bullish trail break with a still-falling median may represent:
A temporary rebound.
A liquidity sweep.
Noise inside a larger bearish structure.
Requiring the median to rise adds another layer of confirmation.
The trade-off is lag.
A genuine reversal may cross the trail before the rolling median has clearly changed direction.
Slope Lookback
Slope Lookback controls how far back the median is compared.
Lower values:
Respond more quickly.
Require only a very local median turn.
Higher values:
Require a broader directional shift.
Produce stronger confirmation.
Can delay reversals.
This same lookback is also used in the visual slope-strength calculation even when slope confirmation itself is disabled.
Break Trail On Flips
When enabled, the displayed trail is temporarily hidden on the actual regime-flip bar.
This creates a visual break between:
The previous regime’s trail.
The new regime’s trail.
Without the break, the plotting engine can draw a connecting segment from one side of the market to the other.
That connection has no analytical meaning.
Break Trail On Flips affects visualization only.
It does not affect:
Trend state.
Raw bands.
Trail calculations.
Signals.
Robust trend structure
The complete structural model can therefore be summarized as:
Rolling Median determines robust center.
MAD determines robust dispersion.
MAD Scale calibrates the dispersion.
Deviation Factor determines band distance.
Optional ATR floor prevents excessive compression.
Raw bands form the initial envelope.
Ratchet logic creates trailing support and resistance.
Opposite-trail breaks determine regime changes.
Optional median slope confirms those reversals.
This combination is what separates the indicator from simply plotting median ± MAD.
Visual strength model
The script calculates a separate Trend Strength value used only to control the presentation of the gradient and glow.
It does not alter:
Trend direction.
Trail levels.
Flip conditions.
Trend Strength combines:
Price distance from the active trail.
Absolute rolling-median slope.
Distance Strength
The script first measures:
Trail Distance = |Close - Active Trail|
This is normalized by the current band width.
The normalized distance is capped when price reaches twice the active band width away from the trail.
Conceptually:
Close to trail = low distance strength.
Far from trail = high distance strength.
This reflects how separated price is from the current structural boundary.
Slope Strength
The indicator also measures:
|Current Median - Median |
This value is normalized by the current band width and capped at one.
The purpose is to compare median movement against the current statistical width.
A steep median relative to the band width produces stronger visual slope strength.
Combined Trend Strength
The final visual strength is:
70% Distance Strength.
30% Median Slope Strength.
and is capped at one.
The distance component receives greater weight because the visual system places more emphasis on how strongly price is separated from the active trail.
Again, this number is not a probability, forecast or additional signal.
It is a visual intensity measure.
Layered gradient
The area between the active trail and current close is divided into several intermediate levels.
The script creates reference points approximately:
15% of the distance from trail to price.
35%.
60%.
82%.
Then the final segment to price.
These create five layered gradient regions.
The layers become progressively more transparent as they move away from the trail.
This gives the trail visual depth without turning the entire area between price and structure into one solid block.
Gradient direction
The geometry of the gradient is determined by whether close is above or below the active trail.
The colour itself comes from the current bullish or bearish trend regime.
The gradient therefore visualizes:
The active trend colour.
The distance between price and trail.
The relative strength of the trend visualization.
The gradient does not determine the regime.
Trend-strength gradient response
Higher Trend Strength reduces transparency in several layers.
This makes the ribbon more visible when:
Price is strongly separated from the trail.
The rolling median is moving meaningfully.
Lower strength produces a softer appearance.
This allows the visual presentation to communicate more than simple bullish or bearish state.
Flip bloom
The indicator includes a temporary post-flip bloom.
The bloom is derived from the number of bars elapsed since the most recent bullish or bearish transition.
Importantly, in the current implementation the bloom begins after the flip bar:
Flip bar: no bloom boost.
1 bar after flip: maximum bloom.
2 bars after flip: reduced bloom.
3 bars after flip: smaller residual bloom.
Afterward: bloom disappears.
The relative bloom strengths are:
1.00
0.55
0.25
This emphasizes the early bars following a newly confirmed regime change.
Why bloom after the flip?
The flip itself can optionally contain a break in the trail.
Applying the bloom to the following bars emphasizes the newly established active trail rather than drawing a large effect around a temporarily hidden flip point.
The bloom is cosmetic.
It does not modify the underlying calculations.
Trail glow
The active trail can also display a persistent glow.
Glow width is based on:
ATR(14) × a factor that increases with Trend Strength
This ATR(14) is fixed for visualization and is independent of the user-selected ATR Length used by the optional minimum-width floor.
The glow therefore becomes slightly wider as visual trend strength increases.
Two layers are used:
A tighter inner glow.
A broader outer glow.
The inner glow responds more strongly to Trend Strength and post-flip bloom.
Rolling Median display
The rolling median can be displayed independently from the trail.
This is useful for studying the difference between:
The current robust center.
The statistical raw bands.
The ratcheting trend trail.
During a bullish regime, the active Lower Trail can remain below the rolling median.
During a bearish regime, the active Upper Trail can remain above it.
The median is not itself the trend signal.
Raw MAD Bands display
The raw upper and lower MAD bands can also be shown.
These lines make it easier to see how the trailing logic differs from the unrestricted statistical envelope.
Raw bands:
Can move in either direction.
Trailing bands:
Can ratchet in only one direction while their persistence condition remains active.
The gap between raw and trailing levels illustrates the hysteresis introduced by the trend logic.
Trend candles
The script can redraw candles on the main chart using the active trend colour.
Bullish regime:
Uses the selected Bullish colour.
Bearish regime:
Uses the selected Bearish colour.
The candle colour represents the persistent trail regime, not whether each individual candle closed higher or lower.
A bearish candle can therefore remain bullish-coloured while the broader MAD Trail regime remains bullish.
Signal markers
Bullish and bearish markers appear only on complete transitions between established regimes.
A bullish marker requires:
Previous trend = bearish.
Current trend = bullish.
A bearish marker requires:
Previous trend = bullish.
Current trend = bearish.
Initial trend assignment does not generate a flip marker.
How to interpret the indicator
Bullish regime
A bullish state means price has previously broken above the opposing Upper Trail and the Lower Trail is now active.
The Lower Trail can be interpreted as:
Dynamic trend support.
A structural invalidation reference.
A trailing regime boundary.
Bearish regime
A bearish state means price has broken below the opposing Lower Trail and the Upper Trail is active.
The Upper Trail can be interpreted as:
Dynamic resistance.
A bearish invalidation reference.
A trailing regime boundary.
Price close to trail
When price approaches the active trail:
Visual distance strength decreases.
The gradient becomes softer.
The market is closer to the regime boundary.
This does not guarantee a reversal.
A healthy trend can repeatedly retest its active trail.
Price far from trail
When price moves substantially away:
Distance Strength rises.
The visual effect becomes stronger.
This indicates greater separation from the active structural boundary.
It should not automatically be interpreted as a better entry.
A market can be strongly extended and simultaneously close to exhaustion.
Median and trail rising together
During a bullish regime, a rising median combined with a rising Lower Trail indicates:
The robust center is moving upward.
The structural support boundary is also advancing.
This represents cleaner directional alignment.
Median flattening while trail remains bullish
The persistent regime can remain bullish while the median begins flattening.
This indicates:
The trend has not yet been invalidated.
But the robust center is no longer advancing as strongly.
The visual slope-strength component may weaken under this condition.
Raw band expansion
If MAD increases:
Raw bands widen.
Trail reset levels can move farther away.
This means recent source values are becoming more dispersed around the median.
Raw band contraction
If MAD falls:
The raw envelope tightens.
If the ATR floor is disabled, the structure can become substantially narrower.
If the ATR floor is enabled, contraction stops once the selected minimum width is reached.
How to use the indicator
1. Trend regime filter
Use the persistent trail state as directional context:
Bullish trail regime = prioritize long-side setups.
Bearish trail regime = prioritize short-side setups.
The trail does not define a complete trading system by itself.
2. Pullback structure
During a bullish regime, the Lower Trail can provide a dynamic reference for deeper pullbacks.
During a bearish regime, the Upper Trail can provide a reference for rallies.
The farther price moves from the trail, the greater the current structural separation.
3. Regime transitions
Bullish and bearish flips identify moments when price has crossed completely through the opposing robust-deviation trail.
These may be used as:
Trend-change alerts.
Confirmation for another entry method.
Potential exit conditions.
4. Median confirmation
Users who want more selective signals can enable Median Slope Confirmation.
This can be especially useful when:
The market is choppy.
Price frequently sweeps through statistical boundaries.
5. Pure robust-volatility mode
Disable the ATR Minimum Width to make band width depend only on:
Rolling MAD.
MAD Scale.
Deviation Factor.
This produces the purest version of the model.
6. Hybrid robust-volatility mode
Enable ATR Minimum Width when the MAD channel becomes too narrow for the instrument or timeframe.
This preserves MAD as the primary engine while adding a conventional range-based safety floor.
Input guide
Source
Series used for the rolling median and MAD calculation.
MAD Lookback
Controls the number of observations used for the rolling median and dispersion estimate.
Shorter values adapt faster.
Longer values create a broader and more stable distribution.
MAD Scale
Multiplier applied directly to raw MAD.
The commonly cited normal-distribution consistency factor is approximately 1.4826; the script default is 1.4655.
Deviation Factor
Controls the final width of the MAD envelope.
ATR Minimum Width
Prevents the active band width from falling below an ATR-derived floor.
ATR Length
Controls the ATR used by the optional floor.
ATR Floor
Controls the minimum width as a multiple of ATR.
Median Slope Confirmation
Requires the rolling median to move in the direction of a proposed trend flip.
Slope Lookback
Controls how far back the current median is compared.
It also influences the visual slope-strength calculation.
Flip Trigger
Selects Close or Source for trail-break detection.
Break Trail On Flips
Creates a visual discontinuity on transition bars.
How this differs from a standard Supertrend
A conventional Supertrend generally uses:
A price midpoint such as HL2.
ATR as the full band-width model.
MAD Volatility Trail instead uses:
Rolling median as its center.
Median Absolute Deviation as its primary width.
ATR only as an optional minimum floor.
The trail mechanics are conceptually related, but the statistical foundation is different.
How this differs from Bollinger Bands
Bollinger Bands normally use:
A moving average.
Standard deviation.
Symmetrical raw bands.
MAD Volatility Trail uses:
Rolling median.
Median Absolute Deviation.
One-sided trailing bands.
Persistent trend-state logic.
Bollinger Bands are primarily a statistical envelope.
MAD Volatility Trail converts its robust statistical envelope into a trend-regime system.
How this differs from median ± MAD alone
A simple median-MAD indicator would plot:
Median.
Median + MAD width.
Median - MAD width.
Those bands would move freely.
This indicator adds:
Ratchet logic.
Persistent bullish/bearish state.
Opposite-trail break conditions.
Optional median-slope confirmation.
Signals and alerts.
The raw statistical model is therefore only the first stage.
MAD versus ATR
ATR measures the size of trading ranges.
MAD measures dispersion of the selected source around its median.
They can behave very differently.
For example:
A volatile but mean-reverting market can have large ATR with relatively controlled median dispersion.
A persistent directional displacement can produce increasing MAD even if individual candle ranges are moderate.
The optional floor allows both concepts to coexist without replacing the MAD foundation.
Robust statistics and financial markets
Financial return and price distributions frequently contain:
Outliers.
Large jumps.
Skew.
Fat tails.
Mean-and-standard-deviation models remain extremely useful, but robust alternatives can provide different information when unusual observations are present.
Median and MAD belong to a family of robust statistical tools designed to reduce sensitivity to extreme sample values.
This does not make the resulting indicator immune to market shocks.
If enough of the rolling window moves, the median and MAD will also move.
The advantage is primarily that one isolated observation has less influence.
Strengths
Uses an exact rolling median.
Uses exact Median Absolute Deviation rather than an approximation.
More resistant to isolated outliers than mean/standard-deviation envelopes.
Provides a configurable MAD scale.
Supports a pure MAD or MAD-plus-ATR hybrid width.
Converts robust statistics into persistent trend boundaries.
Uses one-sided trail logic to reduce rapid regime switching.
Provides optional median-direction confirmation.
Separates signal logic from visual strength.
Includes dynamic gradient, glow and post-flip visualization.
Exposes raw MAD, scaled MAD, active band width and Trend Strength in the Data Window.
Limitations
The indicator is reactive rather than predictive.
Robust statistics do not eliminate whipsaws.
A very short MAD Lookback can still react sharply.
A very long lookback can delay adaptation to new regimes.
Median calculations can remain unchanged across several bars and then move discretely as the rolling sample changes.
Higher Deviation Factors reduce reversals but increase confirmation lag.
The ATR floor changes the model from pure MAD dispersion to a hybrid MAD/ATR structure.
Median Slope Confirmation can reject false breaks but also delay genuine reversals.
Extreme readings in the visual-strength system are not probabilities of continuation.
Glow and bloom are cosmetic and should not be treated as separate signals.
Computational considerations
Unlike many moving averages, the exact rolling median and MAD calculations require the script to build and process the values inside the selected window.
For each bar:
The rolling source sample is collected.
Its median is calculated.
Absolute deviations from that median are calculated.
A second median is calculated from those deviations.
Larger MAD Lookbacks therefore require more work than a simple recursive EMA or ATR calculation.
This is the cost of calculating the robust statistics directly.
Causality and live-bar behaviour
The indicator uses current and historical values without intentional future-looking references.
On completed historical bars, the model is causal.
On a live unfinished bar:
The Source can change.
The current rolling median can change.
MAD can change.
Raw bands can change.
A trail break can appear or disappear.
Users who require confirmed regime changes should evaluate signals at bar close.
Data Window
The indicator exposes four useful diagnostic values.
Raw MAD
The unscaled median absolute deviation.
Scaled MAD
Raw MAD multiplied by the selected MAD Scale.
Active Band Width
The actual band width after:
MAD scaling.
Deviation Factor.
Optional ATR minimum floor.
Trend Strength
The visual-strength score expressed from approximately 0 to 100.
This is calculated from trail distance and median movement.
It is not part of the trend-flip logic.
Alerts
The indicator includes:
MAD Trail Bullish: established bearish regime changes to bullish.
MAD Trail Bearish: established bullish regime changes to bearish.
MAD Trail Flip: either regime transition occurs.
Summary
MAD Volatility Trail builds a trend-following regime from robust statistics.
The calculation begins with an exact rolling median of the selected Source.
Rather than measuring dispersion with standard deviation, the script calculates the Median Absolute Deviation:
MAD = Median(|X - Median(X)|)
The raw MAD is scaled and multiplied by a configurable Deviation Factor to create the statistical width around the rolling median.
The resulting raw upper and lower bands are:
Median + Band Width.
Median - Band Width.
An optional ATR minimum floor prevents these bands from becoming excessively narrow during low-dispersion conditions.
The raw envelope is then transformed into one-sided trailing boundaries.
The Lower Trail can ratchet upward while price remains above it, while the Upper Trail can ratchet downward while price remains below it.
These trails create hysteresis and form the actual regime-switching structure.
A bearish regime turns bullish only when the selected trigger breaks above the opposing Upper Trail, optionally while the rolling median itself is rising.
A bullish regime turns bearish only when the trigger breaks below the Lower Trail, optionally while the median is falling.
The active Lower Trail is displayed during bullish regimes and the active Upper Trail during bearish regimes.
A separate visual-strength model measures price-to-trail distance and median slope relative to the active band width. That score controls gradient and glow intensity but does not alter signals.
The result is a robust alternative to conventional mean-, standard-deviation- and ATR-centered trend trails.
Rather than allowing individual extreme prices to dominate its statistical center and dispersion estimate, MAD Volatility Trail uses the median twice: once to define the center of the distribution and again to define the typical absolute distance from that center.
This creates a trend framework designed around robust location, robust dispersion and persistent trailing structure .
Indicador
Adaptive T3 Hull [BackQuant]Adaptive T3 Hull
Overview
Adaptive T3 Hull is a configurable trend-following overlay that combines the lag-compensation structure of a Hull-style moving average with T3 smoothing and several optional mechanisms designed specifically to control overshoot, hooks and oscillating tails.
A conventional Hull construction gains responsiveness by comparing a faster and slower smoother, extrapolating their difference, and then smoothing the result again. This can produce a very responsive trend estimate, but the same lag compensation responsible for that responsiveness can also create exaggerated curvature around sharp reversals.
Adaptive T3 Hull makes that trade-off directly controllable.
The indicator replaces the traditional weighted-moving-average Hull stages with T3 smoothers and expands the basic Hull architecture with:
Adjustable fast/slow length relationships.
Adjustable Hull lag compensation.
Configurable final smoothing geometry.
Curvature-sensitive tail damping.
Optional asymmetric damping around turns.
An adaptive T3 volume factor.
An optional ATR-based velocity limiter.
Optional final lag compensation.
Trend-strength-dependent ribbon intensity.
Tail and curvature diagnostics in the Data Window.
The result is not intended to reproduce a standard HMA exactly. It is a generalized Hull-style framework in which the user can explicitly control the balance between responsiveness, smoothness and overshoot.
Core idea
Most trend smoothers face the same fundamental compromise:
More smoothing reduces noise but increases lag.
More lag compensation improves responsiveness but can create overshoot.
The Hull concept addresses lag by comparing a fast smoother with a slower smoother and projecting the difference forward.
A generalized form can be written as:
Hull Raw = Fast + Compensation × (Fast - Slow)
If Compensation is zero:
Hull Raw = Fast
No additional lag compensation is applied.
If Compensation is one:
Hull Raw = 2 × Fast - Slow
This reproduces the familiar compensation structure used in the standard Hull Moving Average.
Values between zero and one provide partial compensation.
Adaptive T3 Hull defaults to a substantially smaller compensation value. This is deliberate. It reduces the tendency for the projected line to extend beyond the fast smoother during sharp changes in direction.
The remaining responsiveness can then be controlled using the fast-length ratio, T3 characteristics and optional final generalization rather than relying entirely on aggressive Hull extrapolation.
Processing chain
The complete indicator can be understood as the following sequence:
Select the source and main Hull Length.
Derive a fast T3 length from the Fast Length Ratio.
Derive a final smoothing length from a configurable power-law relationship.
Calculate fast and slow T3 smoothers.
Measure velocity and curvature of the fast T3.
Normalize curvature using ATR.
Optionally reduce the active T3 Volume Factor during high curvature.
Recalculate the fast and slow T3 legs with the adaptive factor.
Measure the active curvature state.
Optionally reduce Hull compensation when curvature increases.
Construct the compensated fast-minus-slow T3 Hull.
Smooth that result through another T3 stage.
Optionally apply a final generalized lag-compensation stage.
Optionally limit extreme one-bar movement using ATR.
Determine trend from the final line slope.
Build a smoothed one-bar-offset ribbon around the result.
Each stage affects a different part of the lag-versus-overshoot problem.
T3 smoothing
The T3 is a multi-stage recursive smoother constructed from a sequence of exponential moving averages.
The script calculates six EMA stages:
E1 = EMA(Source)
E2 = EMA(E1)
E3 = EMA(E2)
E4 = EMA(E3)
E5 = EMA(E4)
E6 = EMA(E5)
Those stages are then combined using coefficients derived from the T3 Volume Factor.
The final T3 has the general form:
T3 = C1×E6 + C2×E5 + C3×E4 + C4×E3
where C1 through C4 change with the Volume Factor.
This construction allows T3 smoothing to maintain substantial smoothness while using coefficient-based compensation to reduce some of the lag created by repeated EMA filtering.
Important: T3 Volume Factor does not use trading volume
Despite its name, the T3 Volume Factor is not calculated from market volume.
It is a coefficient controlling the internal T3 response.
Changing it does not incorporate:
Exchange volume.
Volume profile.
OBV.
Money flow.
It changes how aggressively the internal EMA stages are combined.
Higher values generally increase compensation and responsiveness, but can also increase overshoot.
Lower values generally produce a more restrained and smoother response.
This relationship is particularly important in this indicator because Hull compensation and T3 compensation can interact.
An aggressive T3 followed by aggressive Hull extrapolation can produce substantially more tail behaviour than either technique alone.
Why combine T3 and Hull logic?
Hull-style smoothing and T3 smoothing approach lag reduction differently.
The Hull architecture uses:
A fast smoother.
A slow smoother.
The difference between them.
A final smoothing stage.
T3 uses:
Multiple recursive EMA stages.
A coefficient-controlled combination of those stages.
Adaptive T3 Hull combines both ideas.
Instead of:
Fast WMA.
Slow WMA.
Final WMA.
the indicator uses:
Fast T3.
Slow T3.
Compensated difference.
Final T3.
This produces a smoother underlying structure while retaining the ability to compensate for lag.
However, combining two lag-reduction mechanisms also makes overshoot control more important. Much of the indicator is therefore devoted to regulating that compensation dynamically.
Hull Length
Hull Length establishes the main smoothing horizon.
It is used to derive:
The slow T3 length.
The fast T3 length.
The final smoothing length.
Lower values:
React more quickly.
Track shorter trend changes.
Increase sensitivity to local curvature.
Can generate more frequent directional flips.
Higher values:
Produce broader trend estimates.
Reduce short-term variation.
Increase response delay.
Generally produce more persistent regimes.
Unlike a standard HMA, the relationship between these three smoothing stages is not fixed.
Fast Length Ratio
The fast T3 length is calculated as:
Fast Length = Hull Length × Fast Length Ratio
with the result rounded to a valid integer.
In a conventional Hull structure, the fast stage normally uses approximately half the main length.
Therefore:
Fast Length Ratio = 0.50
reproduces the familiar half-length relationship.
The default configuration uses a larger ratio, making the fast leg closer in length to the slow leg.
This matters because the difference:
Fast T3 - Slow T3
is the quantity used for lag compensation.
If the fast and slow stages are very different:
Their separation can become larger.
Hull compensation becomes stronger.
The resulting line can react faster.
Overshoot potential increases.
If their lengths are closer:
Their separation becomes smaller.
The compensation term becomes more restrained.
The final line generally becomes smoother.
Fast Length Ratio is therefore another direct control over the aggressiveness of the Hull projection.
Hull Compensation
Hull Compensation controls how much of the fast-versus-slow difference is added back to the fast T3.
The underlying formula is:
Hull Raw = Fast T3 + Effective Compensation × (Fast T3 - Slow T3)
Before adaptive damping is applied, Effective Compensation begins from the Hull Compensation input.
Compensation = 0
The raw line becomes the fast T3 itself.
No Hull-style extrapolation occurs.
Compensation = 1
The calculation becomes:
2 × Fast T3 - Slow T3
which matches the standard Hull lag-compensation form.
Compensation between 0 and 1
Only part of the fast-slow separation is extrapolated.
This creates a middle ground between:
Pure fast smoothing.
Full Hull compensation.
Compensation above 1
The difference is extrapolated even more aggressively than a conventional Hull construction.
This can create a highly responsive line, but it also increases the likelihood of:
Overshoot.
Hooks.
Large tails after sharp turns.
The default is intentionally conservative relative to a standard Hull.
What are Hull tails?
Hull-style moving averages can develop a distinctive oscillating or hooked appearance around strong reversals.
This occurs because the lag-compensation term is effectively extrapolating the difference between two smoothers.
Imagine the fast smoother accelerating upward while the slow smoother is still catching up.
The difference:
Fast - Slow
becomes positive.
Adding that difference to the fast smoother projects the result even further upward.
When price abruptly reverses, the fast smoother begins turning first while the slow smoother remains elevated.
The compensation term can then change rapidly and cause the completed Hull to:
Extend beyond the fast line.
Hook sharply.
Reverse with excessive curvature.
This is not necessarily an error in the Hull formula. It is a consequence of aggressive lag compensation.
Adaptive T3 Hull includes several independent tools for reducing this behaviour.
Final Hull smoothing
After the fast and slow T3 legs are combined, the raw Hull is smoothed again.
The final smoothing length is calculated from:
Length^Hull Smoothing Exponent × Final Smoothing Multiplier
This generalizes the standard Hull square-root stage.
A conventional HMA normally uses approximately:
sqrt(Length)
which is equivalent to:
Length^0.50
before rounding.
Hull Smoothing Exponent
The Hull Smoothing Exponent controls how strongly the final smoothing length grows as the main Hull Length increases.
Exponent = 0.50
Reproduces the square-root relationship used in the conventional Hull construction.
Exponent below 0.50
Produces a shorter final smoothing stage, particularly at larger main lengths.
This generally:
Increases responsiveness.
Allows more of the compensated movement through.
Exponent above 0.50
Creates a longer final smoothing stage.
This generally:
Reduces local variation.
Smooths more aggressively.
Adds response delay.
The script allows this relationship to be generalized instead of forcing the standard square-root rule.
Final Smoothing
Final Smoothing applies an additional multiplier to the derived root length:
Final Length = Length^Exponent × Root Multiplier
This gives a second level of control over the final stage without changing the underlying power-law relationship.
Higher values:
Increase final smoothing.
Reduce local hooks.
Slow the line.
Lower values:
Decrease final smoothing.
Increase responsiveness.
Allow more short-term curvature through.
The Smoothing Exponent controls how smoothing scales with Hull Length.
The Final Smoothing multiplier controls the overall magnitude of that final stage.
Curvature measurement
Adaptive tail damping requires a way to determine when the fast T3 is changing direction unusually quickly.
The indicator first calculates velocity:
Velocity = Fast T3 - Previous Fast T3
Previous velocity is:
Previous Velocity = Previous Fast T3 - Fast T3 two bars ago
Curvature is then approximated as the absolute change in velocity:
Curvature = |Velocity - Previous Velocity|
This is a discrete second-difference concept.
Velocity describes how quickly the smoother is moving.
Curvature describes how quickly that velocity itself is changing.
For example:
A steadily rising line can have positive velocity but low curvature.
A line suddenly flattening after a strong rise can have high curvature.
A sharp reversal can produce very high curvature.
This makes curvature particularly useful for detecting the conditions in which Hull overshoot tends to appear.
ATR normalization
Raw curvature is not directly comparable across instruments.
A $10 curvature movement is enormous for one market and negligible for another.
The script therefore normalizes curvature using ATR:
Normalized Curvature = Curvature / ATR
The result is capped at 1.
This creates an adaptive pressure measure between approximately:
0 = little curvature relative to recent range.
1 = very large curvature relative to recent range.
ATR is calculated using the Damping Normalization length.
This normalized curvature drives several optional adaptive mechanisms.
Damping Normalization
Damping Normalization controls the ATR period used when converting curvature into a relative value.
Short values:
Make the normalization respond rapidly to current volatility.
Allow damping pressure to change quickly.
Longer values:
Create a more stable volatility baseline.
Reduce rapid changes in normalized curvature.
This setting does not smooth the final T3 Hull directly.
It changes how the adaptive systems interpret curvature.
Adaptive Tail Damping
Adaptive Tail Damping dynamically reduces Hull Compensation when curvature becomes large.
The process can be summarized as:
Effective Compensation = Hull Compensation × (1 - Damping Pressure × Damping Strength)
When curvature is low:
Damping Pressure approaches zero.
Effective Compensation remains close to the selected Hull Compensation.
When curvature becomes large:
Damping Pressure increases.
Effective Compensation is reduced.
This means the indicator deliberately removes some of its lag compensation precisely when the fast T3 is bending sharply.
Why reduce compensation during curvature?
Hull compensation is most useful when the fast and slow smoothers are moving consistently in the same directional structure.
During a smooth trend:
The fast line leads the slow line.
Their separation can be used to reduce lag.
During a sharp turn:
The fast line may reverse before the slow line.
Their separation can become a poor estimate of useful forward compensation.
Extrapolating the full difference can create overshoot.
Adaptive damping therefore treats high curvature as a reason to trust the Hull extrapolation less.
Damping Strength
Damping Strength determines how much curvature can reduce Hull compensation.
At zero:
Curvature has no effect on compensation.
As the value increases:
High-curvature events remove progressively more compensation.
The line becomes more restrained around sharp turns.
At a Damping Strength of 1 and maximum normalized curvature, compensation can theoretically be reduced all the way toward zero.
This does not stop the underlying T3 from moving.
It removes the additional Hull extrapolation.
Asymmetric Turn Damping
By default, curvature damping can apply whenever the fast T3 experiences significant curvature.
Asymmetric Turn Damping makes the condition more selective.
When enabled, damping pressure is only applied when the current velocity is moving against the previous directional pace.
Conceptually:
A previously rising fast T3 is damped when its upward velocity begins weakening or reversing.
A previously falling fast T3 is damped when its downward velocity begins weakening or reversing.
This allows strong acceleration in the existing direction to retain more compensation while focusing the damping mechanism around deceleration and turning behaviour.
The purpose is to distinguish:
Curvature caused by trend acceleration.
Curvature caused by trend exhaustion or reversal.
This can preserve responsiveness during strong continuation while still suppressing tails around turns.
Adaptive T3 Volume Factor
Adaptive T3 Volume Factor provides a second curvature-sensitive damping mechanism.
Instead of changing the Hull compensation, this feature changes the internal T3 coefficient itself.
The active factor is approximately:
Active VF = Base VF × (1 - Normalized Curvature × VF Damping Strength)
subject to the configured minimum.
When curvature is low:
Active VF remains near the selected T3 Volume Factor.
When curvature rises:
Active VF is reduced.
The T3 becomes less aggressively compensated.
This attacks overshoot earlier in the processing chain.
Hull damping versus VF damping
The two mechanisms affect different stages.
Adaptive Tail Damping
changes how much:
Fast T3 - Slow T3
is extrapolated.
Adaptive T3 Volume Factor
changes how the T3 smoothers themselves are constructed.
Using both means curvature can reduce:
The aggressiveness of each T3 leg.
The aggressiveness of the Hull compensation between those legs.
This can strongly suppress tails but may also reduce responsiveness.
The controls are therefore optional and independently adjustable.
VF Damping Strength
VF Damping Strength controls how strongly curvature reduces the T3 Volume Factor.
Higher values:
Produce larger reductions during sharp curvature.
Increase smoothing around turns.
Can reduce T3 overshoot more aggressively.
Lower values:
Keep Active VF closer to the base setting.
Preserve more of the original T3 response.
Minimum VF
Minimum VF prevents the adaptive mechanism from reducing the active coefficient indefinitely.
It defines the lower bound used when Adaptive T3 Volume Factor is active.
This keeps the filter within a controlled response range during extreme curvature.
If the selected base Volume Factor is already below the requested minimum, the script does not force it upward above the base value.
Generalize Final Hull
Generalize Final Hull adds another optional lag-compensation stage after the main T3 Hull has already been completed.
A second smoothed version of the completed Hull is calculated.
The final target then becomes:
Hull Target = Hull Base + Generalization × (Hull Base - Second Hull)
This uses the same broad idea as Hull compensation:
Compare a faster estimate with a slower version.
Add part of their difference back to the faster estimate.
At zero Generalization:
The stage has no effect.
As Generalization increases:
The final result becomes more responsive.
Lag is reduced further.
Overshoot potential increases.
This option exists because the earlier tail controls allow the user to reduce aggressive compensation in the main Hull construction and, if desired, reintroduce a smaller amount of controlled responsiveness at the end.
Generalization
Generalization controls the amount of final compensation.
Lower values create subtle lag reduction.
Higher values increasingly extrapolate the difference between the first and second completed Hull smoothers.
This feature should be considered one of the more aggressive responsiveness controls in the indicator.
If the objective is maximum tail suppression, it can be left disabled.
Velocity Limiter
The Velocity Limiter addresses a different problem.
Curvature damping changes how the line is calculated.
The Velocity Limiter places a direct cap on how far the completed line is allowed to move in one bar.
The maximum permitted movement is:
Maximum Step = ATR × Max ATR / Bar
The desired change is:
Delta = Hull Target - Previous T3 Hull
That change is clamped between:
-Maximum Step
+Maximum Step
The final T3 Hull then advances by only the permitted amount.
Why use a velocity limiter?
Occasionally, a large price shock or a combination of aggressive settings can cause the completed Hull target to jump sharply.
The limiter acts as a final mechanical speed limit.
It can reduce:
Single-bar jumps.
Extreme hooks.
Shock-driven movement.
However, this comes with a clear trade-off.
If the market genuinely reprices very quickly, the limiter deliberately prevents the trend line from following the full move immediately.
It therefore introduces controlled lag.
Max ATR / Bar
This setting determines the maximum permitted single-bar movement in ATR units.
For example:
0.35 allows the completed line to move by no more than 0.35 ATR in one bar.
Lower values:
Create stronger movement suppression.
Produce smoother transitions.
Can significantly delay response to genuine breaks.
Higher values:
Interfere less often.
Allow larger legitimate moves.
The limiter is disabled by default because it is a strong constraint.
How the tail controls work together
The script provides several different ways to reduce tail behaviour because overshoot can originate at multiple stages.
Fast Length Ratio
Reduces fast-versus-slow separation.
Hull Compensation
Directly controls extrapolation of that separation.
Final Smoothing
Smooths the compensated output more heavily.
Adaptive Tail Damping
Reduces Hull compensation during curvature.
Asymmetric Turn Damping
Restricts that damping mainly to deceleration and turning behaviour.
Adaptive T3 Volume Factor
Makes the underlying T3 calculations more conservative during curvature.
Velocity Limiter
Caps the final single-bar movement.
Generalization
Moves in the opposite direction by optionally adding some final lag compensation back.
These controls are intentionally modular.
A user does not need to enable all of them.
Default design philosophy
The default settings intentionally do not reproduce a standard Hull Moving Average.
A standard Hull-like configuration would approximately use:
Fast Length Ratio near 0.50.
Hull Compensation near 1.00.
Hull Smoothing Exponent near 0.50.
Final Smoothing near 1.00.
The default Adaptive T3 Hull uses a much more restrained compensation structure.
This shifts the design away from maximum lag cancellation and toward smoother trend tracking with reduced tail behaviour.
The advanced controls then allow users to progressively move the model toward either:
More responsiveness.
More stability.
Trend determination
Trend direction is determined directly from the slope of the completed T3 Hull.
If:
Current T3 Hull > Previous T3 Hull
the direction becomes bullish.
If:
Current T3 Hull < Previous T3 Hull
the direction becomes bearish.
If the line is unchanged:
The previous state persists.
The trend does not depend on price crossing the line.
It depends on whether the adaptive T3 Hull itself is rising or falling.
Long and short signals
A long signal occurs when direction changes into the bullish state.
A short signal occurs when direction changes into the bearish state.
The markers therefore identify:
A change in slope regime.
They do not represent:
Guaranteed entries.
Price targets.
Stop levels.
Because the signal is based on local slope, more responsive configurations will naturally produce more flips during sideways conditions.
Ribbon construction
The optional band is not a conventional upper-and-lower volatility channel.
The main line is the current T3 Hull.
The secondary ribbon reference is calculated from a smoothed version of the previous-bar T3 Hull :
Ribbon Reference = WMA(T3 Hull , Band Smoothing)
The area between these two lines is filled with a gradient.
This creates visual separation between:
The current adaptive trend estimate.
A delayed and smoothed reference to its prior values.
The band therefore functions as a trend ribbon rather than a statistical volatility envelope.
Band Smoothing
Band Smoothing controls the WMA applied to the one-bar-offset Hull series.
Lower values:
Keep the ribbon reference close to the main line.
Produce a tighter band.
Respond quickly to direction changes.
Higher values:
Create a slower reference.
Widen the visual separation during sustained movement.
Create a smoother ribbon.
This input affects the visualization only.
It does not change:
The T3 Hull calculation.
Trend direction.
Signals.
Trend Strength
The indicator also calculates a normalized trend-velocity measure for visualization.
Raw strength is based on:
|Current T3 Hull - Previous T3 Hull| / ATR
and is multiplied by the Strength Sensitivity input.
The result is capped at 1 and then smoothed with an EMA.
This produces a normalized value from approximately:
0 = very little line movement relative to ATR.
1 = strong line movement relative to ATR.
This is a measure of trend-line velocity , not a statistical probability that the trend will continue.
Strength Smoothing
Strength Smoothing controls how quickly the visual strength estimate changes.
Lower values:
React quickly to acceleration and deceleration.
Create faster ribbon-intensity changes.
Higher values:
Produce steadier strength visualization.
Reduce flickering in the gradient.
It does not affect the underlying trend calculation.
Strength Sensitivity
Strength Sensitivity determines how quickly line velocity reaches the maximum normalized strength.
Higher values:
Cause smaller ATR-normalized movement to appear strong.
Increase gradient intensity more easily.
Lower values:
Require greater movement before maximum visual intensity is reached.
Strength-Weighted Gradient
When disabled, the ribbon uses a fixed gradient transparency.
When enabled, gradient intensity changes with Trend Strength.
As the T3 Hull moves more quickly relative to ATR:
The near portion of the ribbon becomes more visible.
The broader gradient becomes stronger.
When trend velocity is weak:
The ribbon becomes more subdued.
This is purely a visualization feature.
It does not alter:
Direction.
Signals.
Smoothing.
Tail damping.
Trend candles
The indicator can recolor the main chart candles according to the active T3 Hull slope state.
Bullish trend = selected Long Color.
Bearish trend = selected Short Color.
The candle colour describes the indicator regime, not the individual candle’s own open-to-close direction.
A bearish candle can therefore remain bullish-coloured while the T3 Hull is still rising.
Tail diagnostics
Several internal values are exposed in TradingView’s Data Window.
These provide insight into how the adaptive model is currently behaving.
Effective Hull Compensation
Shows the compensation actually being used after adaptive tail damping.
If adaptive damping is disabled:
It remains equal to Hull Compensation.
If damping is active:
It falls below the base value when curvature pressure increases.
This is useful for seeing when the indicator is automatically becoming more conservative.
Active T3 Volume Factor
Shows the T3 coefficient currently being used.
If Adaptive T3 Volume Factor is disabled:
It remains equal to the base Volume Factor.
When enabled:
It can decrease during high curvature.
Normalized Curvature
Shows the current curvature estimate after ATR normalization.
Values closer to 1 represent greater changes in fast-T3 velocity relative to recent range.
Trend Strength
Shows the smoothed normalized T3 Hull velocity as a percentage.
This is the same quantity used by the optional Strength-Weighted Gradient.
Tail Overshoot
The script also measures whether the final T3 Hull has extended beyond the fast T3 in the direction of the fast/slow separation.
An upper overshoot occurs when:
Fast T3 is above Slow T3.
Completed T3 Hull is above Fast T3.
A lower overshoot occurs when:
Fast T3 is below Slow T3.
Completed T3 Hull is below Fast T3.
When this happens, Tail Overshoot reports:
|T3 Hull - Fast T3| / ATR
This expresses the size of the overshoot in ATR units.
A value of zero means the completed Hull is not currently beyond the fast T3 under that definition.
This diagnostic is particularly useful when tuning:
Hull Compensation.
Damping Strength.
Fast Length Ratio.
Adaptive VF.
Final Smoothing.
Generalization.
How to interpret the indicator
Rising T3 Hull
A rising line indicates a bullish trend state.
The model’s completed combination of T3 smoothing, Hull compensation and any active damping controls is moving upward.
Falling T3 Hull
A falling line indicates a bearish trend state.
Smooth persistent slope
A stable slope with few direction changes generally indicates a cleaner trend environment for this style of filter.
Frequent colour changes
Rapid bullish/bearish transitions generally indicate:
Sideways price action.
A very responsive configuration.
Insufficient smoothing for the current market.
High normalized curvature
High curvature means the fast T3’s velocity is changing rapidly relative to ATR.
If adaptive controls are enabled, this is where:
Hull compensation may decrease.
T3 Volume Factor may decrease.
High tail overshoot
A larger Tail Overshoot value indicates the completed Hull has moved materially beyond the fast T3.
If the objective is a less tail-heavy line, possible adjustments include:
Reduce Hull Compensation.
Increase Final Smoothing.
Increase Fast Length Ratio.
Increase Damping Strength.
Enable Adaptive T3 Volume Factor.
Reduce or disable Generalization.
Enable the Velocity Limiter.
How to use the indicator
1. Trend regime filter
The most direct use is as a slope-based regime filter:
Rising T3 Hull = bullish trend state.
Falling T3 Hull = bearish trend state.
This can be combined with independent entry logic.
2. Trend transition signals
Long and short markers identify when the adaptive line changes slope direction.
These can be used as:
Regime-change alerts.
Confirmation for another setup.
Potential trailing-exit conditions.
They are not standalone guarantees of a sustained reversal.
3. Pullback reference
During a persistent trend, the T3 Hull can act as a smoothed directional reference.
Price returning toward the line while the line continues to slope in the original direction may represent a pullback within the existing regime.
4. Ribbon expansion
The distance between the current T3 Hull and its delayed WMA reference can visually highlight persistent movement.
A stronger ribbon separation can occur when the current adaptive trend estimate is moving away from its delayed historical reference.
5. Tail tuning
The Data Window diagnostics allow the indicator to be treated as a filter-design tool.
Users can observe:
When compensation is being damped.
How strongly curvature is elevated.
Whether the completed line is overshooting.
How the active T3 coefficient changes.
This can make parameter changes easier to understand than tuning solely by appearance.
Suggested tuning approaches
Smooth / reduced-tail configuration
For a calmer trend line:
Use lower Hull Compensation.
Use a larger Fast Length Ratio.
Increase Final Smoothing.
Enable Adaptive Tail Damping.
Use moderate or higher Damping Strength.
Leave Generalization disabled.
If strong shocks still create large movements:
Enable the Velocity Limiter.
Responsive configuration
For faster behaviour:
Reduce Fast Length Ratio toward the traditional half-length relationship.
Increase Hull Compensation.
Reduce Final Smoothing.
Reduce the Hull Smoothing Exponent.
Use a more aggressive T3 Volume Factor.
These changes generally increase overshoot risk.
Adaptive configuration
For responsiveness in normal conditions with additional protection near turns:
Use moderate Hull Compensation.
Enable Adaptive Tail Damping.
Enable Asymmetric Turn Damping.
Optionally enable Adaptive T3 Volume Factor.
This allows stronger compensation during smooth directional movement while automatically reducing it when the line begins to decelerate or turn.
Maximum tail-control configuration
For very aggressive tail suppression:
Low Hull Compensation.
Higher Final Smoothing.
Adaptive Tail Damping enabled.
Higher Damping Strength.
Adaptive T3 Volume Factor enabled.
Generalization disabled.
Velocity Limiter enabled.
This can create a very stable line, but the cost is additional lag.
How this differs from a standard Hull Moving Average
A conventional HMA normally uses:
WMA at half length.
WMA at full length.
2 × Fast - Slow lag compensation.
Final WMA around sqrt(Length).
Adaptive T3 Hull changes every major part of that architecture:
T3 replaces WMA.
Fast Length Ratio is configurable.
Hull Compensation is configurable.
The final smoothing exponent is configurable.
Final smoothing has an additional multiplier.
Compensation can adapt to curvature.
T3 behaviour can adapt to curvature.
Final movement can be ATR-limited.
An additional generalized compensation stage can be enabled.
It is therefore better understood as a generalized adaptive Hull framework than as a conventional HMA with a different smoothing length.
How this differs from a normal T3
A standard T3 produces one smoothed price estimate from repeated EMA stages and a fixed Volume Factor.
Adaptive T3 Hull uses multiple T3 calculations in a Hull-style structure:
Fast T3.
Slow T3.
Compensated fast-slow projection.
Final T3 smoothing.
It can also dynamically alter the T3 factor according to curvature.
The T3 is therefore a building block inside the larger trend model.
How this differs from simply smoothing an HMA
Applying an additional moving average to an HMA can reduce its tails, but it also adds lag after the overshoot has already occurred.
Adaptive T3 Hull attacks the problem at several earlier stages.
It can:
Reduce the fast-slow separation.
Reduce compensation itself.
Reduce compensation specifically around sharp turns.
Reduce the T3 factor during curvature.
Change the final Hull smoothing geometry.
Limit extreme final movement.
This provides more control than applying one additional smoothing layer to a completed HMA.
Parameter interaction
Many settings interact strongly.
Fast Ratio + Hull Compensation
A low Fast Ratio creates greater separation between fast and slow legs.
Combining that with high Hull Compensation can produce aggressive extrapolation.
Hull Compensation + Adaptive Damping
Hull Compensation defines the maximum starting compensation.
Adaptive damping determines how much of it survives during curvature.
T3 Volume Factor + Hull Compensation
Both can contribute to lag reduction.
High values in both stages may amplify overshoot.
Final Smoothing + Generalization
Final Smoothing adds lag and stability.
Generalization removes some of that lag again.
Using both allows the user to create a smooth base and then selectively reintroduce responsiveness.
Adaptive VF + Adaptive Hull Damping
Both respond to curvature but at different stages.
Enabling both can create strong protection around turns.
Velocity Limiter + all other controls
The Velocity Limiter is applied near the end of the pipeline.
It can therefore override an aggressive target generated by the preceding calculations.
Input guide
Source
Price series used by the complete indicator.
Hull Length
Primary calculation horizon.
T3 Volume Factor
Controls the internal T3 coefficient structure. It does not use trading volume.
Hull Compensation
Controls how much of the fast-minus-slow T3 separation is added to the fast T3.
Final Smoothing
Multiplies the final Hull smoothing length.
Adaptive Tail Damping
Reduces Hull Compensation during high curvature.
Damping Strength
Controls the amount of compensation reduction.
Damping Normalization
ATR horizon used to normalize curvature.
Fast Length Ratio
Controls the fast T3 length relative to the main Hull Length.
Hull Smoothing Exponent
Controls the power-law relationship used to derive the final smoothing length.
Asymmetric Turn Damping
Restricts curvature damping primarily to deceleration and turning behaviour.
Adaptive T3 Volume Factor
Reduces the T3 coefficient during high curvature.
VF Damping Strength
Controls how strongly curvature reduces the active T3 factor.
Minimum VF
Limits how far the adaptive T3 factor can be reduced.
Velocity Limiter
Caps final one-bar T3 Hull movement using ATR.
Max ATR / Bar
Defines the maximum movement allowed by the Velocity Limiter.
Generalize Final Hull
Enables an additional lag-compensation stage after the main T3 Hull.
Generalization
Controls the strength of that final compensation.
Strength-Weighted Gradient
Allows ribbon intensity to vary with normalized T3 Hull velocity.
Strength Smoothing
Smooths the visual trend-strength measure.
Sensitivity
Controls how quickly ATR-normalized movement reaches maximum visual strength.
Band Smoothing
Controls the delayed WMA reference used to build the ribbon.
Strengths
Combines T3 smoothing with a generalized Hull framework.
Directly exposes Hull lag compensation as a user control.
Provides multiple independent methods for reducing oscillating tails.
Uses ATR-normalized curvature for adaptive behaviour.
Can distinguish general curvature from decelerating/turning curvature.
Can adapt the T3 coefficient as well as Hull compensation.
Allows the standard Hull square-root smoothing relationship to be generalized.
Includes an optional ATR-based velocity limiter.
Provides optional final lag compensation for advanced tuning.
Includes real-time tail and curvature diagnostics.
Provides trend-strength-reactive visualization without altering signals.
Limitations
The indicator remains a reactive trend filter rather than a predictive model.
Increasing lag compensation generally increases overshoot risk.
Aggressive tail suppression generally increases lag.
Slope-based signals can whipsaw in ranging markets.
The large number of controls creates many interacting parameter combinations.
Over-tuning parameters to one asset or historical period can reduce robustness elsewhere.
The Velocity Limiter can delay response to genuine price shocks.
Generalization can reintroduce overshoot that earlier damping stages removed.
Trend Strength measures line velocity, not probability of continuation.
Tail Overshoot is a diagnostic relative to the fast T3, not a trading signal.
Causality and real-time behaviour
The calculations use current and historical data without intentional future references.
The indicator can therefore be evaluated causally on completed bars.
However, on a live unfinished candle:
The source can change.
The T3 stages can change.
Curvature can change.
Adaptive compensation can change.
The final slope can change.
A long or short signal can appear or disappear before bar close.
Users requiring confirmed trend transitions should evaluate signals on completed candles.
Alerts
The indicator includes three alert conditions:
T3 Hull Long: the completed T3 Hull changes into a rising trend state.
T3 Hull Short: the completed T3 Hull changes into a falling trend state.
T3 Hull Signal: either directional transition occurs.
Summary
Adaptive T3 Hull is a generalized trend smoother built around the idea that Hull-style lag compensation does not need to be fixed.
The model begins with fast and slow T3 smoothers rather than traditional WMAs. Their difference is used to compensate the fast T3 for lag, but the amount of compensation is directly configurable.
This alone allows the user to move continuously between:
A restrained fast T3.
A partially compensated Hull structure.
A conventional 2×fast-minus-slow construction.
More aggressive extrapolation.
The final smoothing stage is also generalized. Instead of forcing the conventional square-root Hull relationship, the user can control both the smoothing exponent and a separate multiplier.
The adaptive systems then focus specifically on the behaviour that often makes Hull-style smoothers difficult to tune: oscillating tails around sharp turns.
The script measures changes in fast-T3 velocity, normalizes that curvature using ATR, and can use the result to:
Reduce Hull compensation.
Reduce the T3 Volume Factor.
Apply damping only around deceleration and turns.
An optional velocity limiter provides a final ATR-based cap on extreme one-bar movement, while an optional generalized compensation stage can reintroduce controlled responsiveness after the main smoothing process.
The final line determines trend through its slope, while a delayed WMA reference forms the optional ribbon. Ribbon intensity can also respond to normalized trend velocity.
Adaptive T3 Hull is therefore designed less as one fixed moving-average formula and more as a configurable filter architecture for exploring the trade-off between lag, smoothness, responsiveness and overshoot .
Its default configuration intentionally favors a less tail-heavy response than a conventional Hull construction, while the advanced controls allow users to move the model toward either greater responsiveness or stronger damping depending on the behaviour they want from the trend filter.
Indicador
Black-Litterman Allocator [BackQuant]# Black-Litterman Allocator
IMPORTANT: Concept / Educational Implementation
Black-Litterman Allocator is a research and educational concept that implements a practical version of the Black-Litterman portfolio-allocation framework inside TradingView and Pine Script.
It is intended to demonstrate how equilibrium priors, covariance estimates, subjective investor views, view confidence, mean-variance optimization, portfolio constraints, volatility targeting and portfolio backtesting can be combined into one visual allocation model.
It should not be interpreted as an institutional-grade portfolio optimizer, automated investment product, portfolio recommendation, or guarantee that the resulting allocation is optimal.
The outputs depend heavily on:
The selected asset universe.
The chart timeframe.
The covariance lookback.
The quality and synchronization of TradingView price data.
The chosen prior-weight scheme.
Risk-aversion assumptions.
The investor views entered by the user.
The confidence attached to those views.
Portfolio constraints.
Volatility-target settings.
Transaction-cost assumptions.
The optional regime filter.
The default universe and default views are examples for demonstrating the framework. They are not investment recommendations.
The script is best treated as a portfolio-allocation laboratory : a way to study how changing assumptions about equilibrium, risk, correlations and expected returns can propagate through a Black-Litterman-style allocation process.
Overview
Black-Litterman Allocator is a 15-asset cross-asset portfolio model that starts with a neutral portfolio prior, reverse-engineers the expected returns implied by that prior, optionally incorporates up to five investor views, solves for a new posterior allocation, applies portfolio constraints and volatility targeting, and then simulates the resulting portfolio through time.
The model follows a broad sequence:
Collect return history for the selected 15-asset universe.
Estimate an annualized covariance matrix.
Stabilize that matrix using diagonal covariance shrinkage.
Construct a prior portfolio.
Estimate the market risk-aversion parameter.
Reverse-optimize the prior into implied equilibrium returns.
Convert investor views into the Black-Litterman P, Q and uncertainty structure.
Blend the prior with those views to obtain posterior expected returns.
Optionally calculate posterior covariance.
Solve a mean-variance portfolio from the posterior.
Apply availability, short-selling, gross exposure and position-size constraints.
Target a desired portfolio volatility.
Apply additional leverage and gross-exposure caps.
Rebalance periodically.
Track the resulting equity curve and portfolio statistics.
The script also provides detailed visualizations showing:
Prior versus final active weights.
Equilibrium versus posterior expected returns.
The impact of individual views.
Current gross and net exposure.
Portfolio volatility and scaling.
Turnover.
Portfolio equity versus a benchmark.
Drawdown and daily returns.
A broad set of performance and risk statistics.
Why Black-Litterman exists
Traditional mean-variance optimization has an important practical weakness.
The optimizer is extremely sensitive to expected-return estimates.
Suppose several assets have similar volatility and correlation characteristics, but one asset is assigned an expected return only slightly higher than the others.
A mathematical optimizer can interpret that small difference very aggressively and allocate an unrealistic amount of capital to that asset.
Small estimation errors in expected returns can therefore produce very large changes in portfolio weights.
This is one reason unconstrained mean-variance portfolios often produce allocations that appear unstable or unintuitive.
The Black-Litterman framework was developed by Fischer Black and Robert Litterman as a way of approaching the problem from the opposite direction.
Instead of beginning with a set of independently estimated expected returns, the framework begins with an equilibrium portfolio and asks:
What expected returns would make this portfolio mathematically optimal?
Those implied returns become the prior.
Investor views are then introduced as controlled deviations from that equilibrium rather than replacing the equilibrium assumptions entirely.
This creates a useful distinction:
Prior = what the portfolio implies before the investor expresses a view.
Views = where the investor believes equilibrium is wrong.
Posterior = the combined result after balancing both sources of information.
That is the central idea behind this indicator.
Important distinction: the prior in this script
In textbook Black-Litterman, the equilibrium portfolio is often represented using market-capitalization weights.
This script is intentionally more flexible.
It provides three different prior schemes:
Equal Weight.
Inverse Volatility.
Manual Weights.
For that reason, the word equilibrium should be interpreted carefully.
If Equal Weight or Inverse Volatility is selected, the prior is a user-selected equilibrium proxy , not necessarily the true global market portfolio.
If Manual Weights is selected and the user enters representative market-cap or benchmark weights, the prior can be made closer to the traditional Black-Litterman interpretation.
This flexibility is intentional because TradingView users may want to study Black-Litterman mechanics without first sourcing a complete set of institutional market-cap weights.
Asset universe
The allocator supports fifteen simultaneously selected assets.
The default universe is designed as a broad cross-asset example containing:
Cryptocurrency.
US equities.
International equities.
Precious metals.
Energy.
The US dollar.
Long-duration Treasury exposure.
The default list includes assets such as Bitcoin, Ethereum, Solana, major equity indices, gold, silver, oil, DXY and TLT.
Every symbol can be replaced by the user.
This allows the framework to be adapted to:
Global macro portfolios.
Equity-sector portfolios.
Cryptocurrency portfolios.
ETF portfolios.
Multi-asset portfolios.
However, all assets should represent actual price series .
Market-capitalization series, synthetic quantities or unrelated non-price data should not be inserted as if they were tradable asset prices, because the resulting returns would contaminate the covariance matrix and portfolio calculations.
Data availability protection
A multi-asset allocator has a specific problem when some assets have shorter histories than others.
Suppose fourteen assets have ten years of data but the fifteenth asset was only listed six months ago.
If missing values are simply converted into zeros, the new asset may appear to have:
Almost no volatility.
Artificially stable returns.
Artificial correlations.
This is especially dangerous when using inverse-volatility weighting, because an asset with incorrectly measured near-zero volatility could receive a very large prior allocation.
The script protects against this by maintaining a separate data-availability state for every asset.
An asset is only admitted into the active universe once it has accumulated at least one complete covariance lookback of valid price history.
Until then:
Its active mask remains disabled.
It receives no prior weight.
It receives no optimized weight.
Views referencing it are ignored.
The allocation table displays it as having no usable data.
This makes the universe dynamic.
A newly listed asset can eventually become active once enough genuine history has accumulated.
Return calculations
The allocator uses two forms of return data for different purposes.
Log returns
Log returns are used for covariance estimation:
Log Return = ln(Price / Previous Price)
These are stored in a rolling history matrix.
Simple returns
Simple returns are used when compounding the simulated portfolio:
Simple Return = Price / Previous Price - 1
This distinction is deliberate.
Log returns are convenient for statistical covariance calculations, while simple returns are appropriate for directly multiplying portfolio wealth through time.
Rolling return-history matrix
The script maintains a rolling matrix containing return history for all fifteen assets.
Each row represents a historical bar and each column represents one asset.
Once the requested covariance lookback has been collected, the matrix acts as the input for the covariance engine.
Rather than recalculating years of historical data from scratch on every bar, the script operates the history as a rolling buffer.
The full Black-Litterman calculation is also performed only on rebalance events rather than continuously.
This is important because:
Covariance estimation is computationally expensive.
Matrix multiplication is expensive.
Matrix inversion is expensive.
TradingView imposes execution limits.
The indicator therefore approximates how a real asset-allocation process is normally operated: weights remain relatively stable between scheduled portfolio reviews and are recomputed at discrete intervals.
Covariance matrix
The covariance matrix is one of the central inputs to the entire model.
For N assets, covariance produces an N × N matrix.
The diagonal contains the variance of each asset.
The off-diagonal entries contain covariance between pairs of assets.
Conceptually:
Positive covariance means two assets tend to move in the same direction.
Negative covariance means they tend to move in opposing directions.
Covariance near zero suggests weaker linear co-movement.
The portfolio does not consider the risk of each asset independently.
Instead, portfolio risk depends on:
Individual asset volatility.
Portfolio weights.
The covariance relationships between every pair of assets.
This is why diversification cannot be measured simply by counting positions.
Ten highly correlated assets may behave more like one large risk exposure than ten independent exposures.
Covariance Lookback
The Covariance Lookback controls how many bars are used to estimate the covariance matrix.
Shorter windows:
Adapt more quickly.
Reflect recent correlation changes.
Contain fewer observations.
Produce noisier covariance estimates.
Longer windows:
Provide more observations.
Create more statistically stable estimates.
Adapt more slowly when correlations change.
This parameter is particularly important when the number of assets is large relative to the number of observations.
With fifteen assets, an extremely short covariance window can create a poorly conditioned or nearly singular matrix.
That can make matrix inversion unstable and produce extreme portfolio weights.
Annualization
The covariance matrix is annualized using the Trading Days per Year input.
The script supports:
252 days.
365 days.
252 is generally appropriate for traditional financial markets operating primarily on weekdays.
365 may be more appropriate for a crypto-only daily portfolio.
Mixed universes require judgement because crypto trades continuously while many traditional markets do not.
The annualization setting affects:
Covariance.
Volatility.
Return statistics.
Risk-aversion estimates.
It should therefore be selected consistently with the universe and timeframe being studied.
Covariance shrinkage
Raw sample covariance matrices can be noisy.
This is particularly problematic when:
The lookback is short.
There are many assets.
Several assets are highly correlated.
Market relationships change rapidly.
The script applies a simple fixed-coefficient shrinkage toward a diagonal covariance target.
The diagonal variances are retained.
The off-diagonal covariance terms are multiplied by:
1 - Shrinkage
Therefore:
Shrinkage = 0
leaves the sample covariance relationships largely unchanged.
Shrinkage = 1
removes the off-diagonal covariance terms and effectively treats the assets as uncorrelated for optimization purposes.
Intermediate values partially reduce estimated correlations.
This is best described as Ledoit-Wolf-style diagonal shrinkage , not as a full automatic Ledoit-Wolf estimator.
A true Ledoit-Wolf implementation estimates an optimal shrinkage intensity statistically.
Here, the user directly controls the shrinkage coefficient.
Why shrinkage can help
Portfolio optimization involves matrix inversion.
If covariance estimates are noisy, the inverse matrix can amplify those errors dramatically.
Shrinkage intentionally sacrifices some estimated correlation detail in exchange for greater numerical stability.
A moderate amount of shrinkage can therefore:
Reduce unstable allocations.
Reduce sensitivity to short-term correlation noise.
Improve matrix conditioning.
Too much shrinkage can also remove genuine diversification information.
The parameter is a bias-versus-variance trade-off.
Safe matrix inversion
Black-Litterman requires several matrix inversions.
Matrices can become singular or nearly singular when:
Assets are highly correlated.
Lookbacks are too short.
Data is incomplete.
The script checks whether the matrix is square and sufficiently non-singular before using a standard inverse.
When necessary, it falls back to a pseudo-inverse.
This does not magically make poor data reliable, but it prevents a singular matrix from immediately destroying the calculation.
A pseudo-inverse should still be interpreted cautiously because the underlying portfolio problem may be poorly conditioned.
Prior portfolio
Before Black-Litterman can estimate equilibrium returns, it requires a prior portfolio.
Three schemes are provided.
Equal Weight
Every active asset receives an equal allocation:
Weight = 1 / Number of Active Assets
This is the simplest prior.
It expresses no preference based on:
Market capitalization.
Volatility.
Expected return.
Its strength is simplicity.
Its weakness is that it assumes every asset deserves the same capital allocation regardless of risk.
Inverse Volatility
Inverse Volatility gives greater prior weight to assets with lower historical volatility.
Conceptually:
Raw Weight ∝ 1 / Volatility
The weights are then normalized.
This produces a risk-oriented prior rather than a capital-oriented prior.
Lower-volatility assets receive more weight.
Higher-volatility assets receive less.
This can be useful for diversified macro portfolios, but it has an important implication:
the quietest asset may dominate the prior.
For example, a bond or currency exposure may receive much more prior weight than cryptocurrency simply because its realized volatility is lower.
This is not a bug.
It is the direct consequence of using inverse volatility as the prior definition.
Manual Weights
Manual mode allows the user to enter fifteen raw numbers corresponding to the fifteen selected assets.
The entries are normalized automatically.
This means the values do not need to sum to 100.
The user can enter:
Percentages.
Market capitalizations.
Benchmark weights.
Relative notional values.
Only their proportions matter.
If the intention is to approximate traditional Black-Litterman market equilibrium, Manual Weights can be used to supply actual or approximate market-cap weights.
Reverse optimization
Once the prior weights are known, the model derives the returns that would make those weights consistent with mean-variance equilibrium.
The implied equilibrium excess-return vector is:
Pi = Delta × Sigma × Wprior
where:
Pi = implied equilibrium excess returns.
Delta = risk-aversion coefficient.
Sigma = covariance matrix.
Wprior = prior portfolio weights.
This is called reverse optimization .
Normal portfolio optimization asks:
Given expected returns, what weights should I own?
Reverse optimization asks:
Given the portfolio weights, what expected returns would justify owning them?
That reversal is one of the key ideas behind Black-Litterman.
Why implied returns matter
Expected returns are difficult to estimate directly.
Historical averages are noisy.
Forecast models disagree.
Small errors can create enormous portfolio changes.
Black-Litterman instead begins from a portfolio that the user considers a reasonable neutral starting point.
The model then backs out the expected returns consistent with that portfolio.
These implied returns become the equilibrium prior against which investor opinions are expressed.
Risk aversion: Delta
Delta controls the relationship between expected return and risk.
Higher Delta means:
Greater assumed aversion to risk.
A larger equilibrium return requirement for a given covariance structure and prior.
Lower Delta implies less risk aversion.
The script provides:
Auto (Implied).
Manual.
Manual Delta
Manual mode allows the user to directly select the risk-aversion coefficient.
This is useful when:
A stable assumption is preferred.
The user is reproducing an external Black-Litterman study.
The portfolio prior is known but a particular Delta is desired.
Auto Delta
Auto mode estimates Delta from the current prior portfolio.
The script estimates:
Prior portfolio variance.
An annualized return estimate over the covariance horizon.
The selected risk-free rate.
It then forms an implied risk-aversion estimate from excess return relative to variance.
The value is constrained to a practical range to prevent extreme estimates from destabilizing the optimizer.
This Auto mode is a practical implementation choice for the concept.
It should not be interpreted as a uniquely correct market risk-aversion estimate.
Tau: uncertainty in the prior
Tau is one of the most important Black-Litterman parameters.
It scales uncertainty in the equilibrium prior.
Conceptually:
Prior Uncertainty = Tau × Sigma
A smaller Tau implies stronger confidence in the equilibrium-return prior.
A larger Tau gives the model more freedom to move away from the prior when investor views are introduced.
In practical terms:
Smaller Tau
Makes the prior harder to move.
Reduces the effect of views.
Larger Tau
Increases prior uncertainty.
Allows views to exert more influence.
Tau should not be interpreted in isolation.
Its effect interacts with:
The covariance matrix.
View confidence.
View direction.
The number of views.
Investor views
The script supports up to five simultaneous investor views.
Each view contains:
A view type.
Asset A.
Optional Asset B.
Expected return Q.
Confidence.
Each view can be:
Off.
Absolute.
Relative.
The expected-return input is interpreted as an annualized expected return or annualized relative return .
Absolute views
An absolute view expresses an opinion about one asset.
For example:
“Asset A will return 10% annually.”
In matrix notation, the corresponding row of the P matrix contains:
+1 for Asset A.
0 for all other assets.
Q then contains:
0.10
for a 10% annual view.
Relative views
A relative view expresses one asset relative to another.
For example:
“Asset A will outperform Asset B by 5% annually.”
The corresponding P row contains:
+1 for Asset A.
-1 for Asset B.
0 elsewhere.
Q becomes:
0.05
This does not necessarily mean Asset A itself must return +5%.
It means:
Expected Return A - Expected Return B = 5%
Relative views are one of the most useful features of Black-Litterman because investors are often more confident about relative relationships than exact absolute returns.
It may be easier to hold the view:
“Gold will outperform equities.”
than:
“Gold will return exactly 12.4%.”
P matrix
The P matrix describes which assets each investor view references.
Each row corresponds to one active view.
Each column corresponds to one of the fifteen assets.
An absolute view creates one non-zero exposure.
A relative view creates a long-versus-short pair.
P therefore translates a verbal market opinion into portfolio mathematics.
Q vector
Q contains the expected return associated with each view.
For absolute views:
Q = expected annual asset return.
For relative views:
Q = expected annual outperformance of A relative to B.
The relationship:
P × Returns = Q
defines what the investor believes.
View confidence
Black-Litterman does not require every opinion to be treated as equally reliable.
Each view therefore receives a confidence value.
Confidence controls its uncertainty.
The basic principle is:
Low confidence = large view uncertainty.
High confidence = small view uncertainty.
The script converts intuitive percentage confidence into an Omega uncertainty term using a confidence mapping related to the Idzorek-style approach to expressing subjective confidence. User-specified confidence was developed precisely to make the otherwise difficult view-uncertainty input more interpretable.
Omega
Omega represents uncertainty in the views.
For each active view, the script first measures the variance of the corresponding view portfolio using:
P × TauSigma × P'
It then scales that variance according to confidence:
Omega = ((1 - Confidence) / Confidence) × View Variance
This has intuitive behaviour.
High confidence
If confidence approaches 100%:
(1 - c) / c approaches zero.
Omega becomes small.
The view receives substantial influence.
Low confidence
If confidence approaches zero:
(1 - c) / c becomes very large.
Omega becomes large.
The view has little effect.
The script bounds confidence away from exactly zero and one for numerical stability.
Why confidence matters
Suppose two investors both believe Bitcoin will outperform gold by 10%.
Investor A has 90% confidence.
Investor B has 20% confidence.
Their view Q is identical.
But their portfolio allocations should not necessarily be identical.
The confidence parameter allows the same directional opinion to produce very different posterior tilts.
This is one of the most useful parts of Black-Litterman.
It separates:
What you believe.
How strongly you believe it.
View disagreement: Q - PΠ
The Views table displays:
Q - PΠ
This measures how far the investor view differs from the equilibrium prior.
Suppose equilibrium already implies that Asset A will outperform Asset B by 8%.
If the user enters a relative view of 9%, the disagreement is only 1%.
The posterior may therefore change only slightly.
If the user instead enters 20%, the disagreement with equilibrium is much larger.
The same confidence level will then produce a much larger posterior adjustment.
This quantity is extremely useful because it shows that the impact of a view depends not only on the view itself, but on how different it is from what the prior already expects.
Posterior expected returns
Once P, Q and Omega have been constructed, the script calculates the Black-Litterman posterior expected-return vector.
Conceptually:
Posterior = Prior + Confidence-Weighted Adjustment
The full adjustment depends on:
Tau.
Sigma.
P.
Q.
Omega.
The disagreement Q - PΠ.
The model therefore does not simply overwrite the expected return of the named asset.
The adjustment can propagate across the entire asset universe through covariance relationships.
This is a fundamental feature of Black-Litterman.
If two assets are strongly related, a view about one may alter the posterior expectation of the other even if that second asset was not explicitly named.
Why views propagate
Suppose the user enters a strong bullish view on one equity index.
If several other equity indices are highly correlated with it, the covariance matrix tells the model that those assets are economically related.
The posterior adjustment therefore does not exist in isolation.
This means:
Views influence related assets.
Portfolio effects depend on covariance.
The same view can produce different tilts under different correlation regimes.
That behaviour is intentional.
No active views
If no usable views are active:
Posterior expected returns remain equal to the equilibrium prior returns.
The allocation is then driven by:
The prior.
Covariance.
Risk aversion.
Portfolio constraints.
Volatility targeting.
This makes the script useful even without discretionary views.
It can be used to study how the prior portfolio behaves under the optimization and risk-management layers by itself.
Posterior covariance
The script can optionally include the Black-Litterman posterior covariance adjustment.
Investor views introduce uncertainty about expected returns.
The posterior covariance calculation incorporates additional uncertainty associated with combining the prior and the views.
When enabled, the optimizer uses this adjusted covariance matrix.
When disabled, optimization uses the original covariance estimate.
The practical effect is usually more subtle than changing the expected-return vector, but it can affect:
Position sizes.
Diversification.
Volatility estimates.
View-driven tilts.
Portfolio optimization
After calculating posterior expected returns, the script solves a mean-variance allocation.
The unconstrained portfolio is conceptually:
w* = (Delta × SigmaPosterior)^-1 × PiPosterior
This converts posterior return expectations and covariance into portfolio weights.
If:
There are no views.
The prior and covariance are internally consistent.
No constraints alter the result.
the solution tends toward the prior portfolio.
Views create deviations away from that starting point.
Why unconstrained weights can be extreme
Mean-variance optimization can produce very large positive or negative positions.
This happens because matrix inversion magnifies differences between:
Expected returns.
Volatility.
Correlations.
If two assets are highly correlated but have slightly different expected returns, the optimizer may create a large long position in one and a large short position in the other.
Mathematically this can be valid.
Practically it may be unusable.
The script therefore applies several layers of portfolio constraints after the raw solution.
Data mask
Assets without sufficient price history receive zero weight regardless of what the raw optimizer produces.
This prevents incomplete covariance columns from entering the live portfolio.
Long-only mode
When Allow Short Weights is disabled:
All negative optimizer weights are clipped to zero.
The remaining positive positions are then normalized.
This converts the portfolio into a long-only allocation.
The result is no longer the exact unconstrained analytical Black-Litterman solution.
That is expected.
Real portfolios frequently require constraints that alter the theoretical optimum.
Short-enabled mode
When shorting is enabled, negative posterior weights are permitted.
This allows:
Long-short portfolios.
Relative-value expressions.
Negative allocations to assets receiving sufficiently weak posterior expectations.
Gross exposure becomes especially important in this mode because a portfolio can have low net exposure while still carrying substantial absolute risk.
For example:
+150% long.
-50% short.
= 100% net exposure.
= 200% gross exposure.
Gross Exposure
The Gross Exposure input controls the target sum of absolute portfolio weights before volatility targeting.
Gross exposure is:
Gross = Sum of |Weight|
This differs from net exposure:
Net = Sum of Weight
For long-only portfolios, gross and net are normally similar.
For long-short portfolios, they can differ significantly.
Volatility targeting
After the portfolio has been normalized, the script estimates total portfolio volatility using:
Portfolio Variance = w' × Sigma × w
Portfolio Volatility = sqrt(Portfolio Variance)
This is a full covariance-aware portfolio volatility calculation.
It does not simply average asset volatility.
The model then calculates a volatility scaling factor:
Volatility Scale = Target Volatility / Estimated Portfolio Volatility
subject to minimum and maximum limits.
If estimated portfolio volatility is below target:
Exposure can increase.
If estimated volatility is above target:
Exposure is reduced.
Why portfolio volatility matters
Suppose two assets each have 20% volatility.
A 50/50 portfolio does not necessarily have 20% volatility.
If the assets are weakly correlated, portfolio volatility may be much lower.
If they are highly correlated, it may remain close to 20%.
Using:
sqrt(w'Σw)
allows the volatility target to account for diversification.
Target Volatility
Target Volatility defines the desired annualized risk level of the portfolio before later hard caps are considered.
Examples might conceptually include:
A lower target for a defensive multi-asset portfolio.
A higher target for a crypto-focused portfolio.
The setting is not automatically appropriate simply because the portfolio reaches it.
A volatility target does not account for:
Tail risk.
Liquidity.
Gap risk.
Regime changes.
Nonlinear derivatives.
It is one risk-control dimension.
Maximum volatility-target leverage
A very low-volatility portfolio can theoretically require enormous leverage to reach a high volatility target.
The Max Vol-Target Leverage setting prevents this.
For example, if the mathematical scaling factor is 6× but the maximum leverage is 3×:
The model uses no more than 3×.
This protects against explosive leverage during unusually quiet covariance estimates.
Maximum weight per asset
After volatility targeting, every individual position is subjected to a hard position-size cap.
This ordering is important.
If the position cap were applied before leverage scaling, the volatility scaler could simply increase the capped position again.
Applying the cap afterward ensures the final position magnitude cannot exceed the selected maximum.
For example:
Max Weight = 30%
means no individual position can remain above 30% after the volatility scaling stage.
Maximum gross exposure after volatility targeting
After individual caps are applied, the portfolio is also checked against a maximum total gross exposure.
If gross exposure exceeds that maximum, every position is scaled downward proportionally.
This provides a second portfolio-level safeguard.
The result is a hierarchy:
Generate raw Black-Litterman weights.
Apply long/short rules.
Normalize initial gross exposure.
Apply volatility targeting.
Cap individual positions.
Cap final gross exposure.
Why the target may not be reached
The volatility target is not guaranteed to be achieved exactly.
Suppose the model wants to increase portfolio exposure enough to reach 15% volatility.
If doing so would violate:
Maximum leverage.
Maximum asset weight.
Maximum gross exposure.
the constraints take priority.
The resulting portfolio may therefore have volatility below the requested target.
This is intentional.
Risk limits are allowed to override the target.
Rebalancing
The complete optimizer does not run on every bar.
The user selects a Rebalance Every N Bars interval.
For a daily chart:
Approximately 21 bars corresponds roughly to one trading month.
Longer rebalance intervals:
Reduce turnover.
Reduce computation.
Allow allocations to persist longer.
Shorter intervals:
React faster to new covariance and view conditions.
Increase turnover.
Increase computational load.
The covariance matrix and Black-Litterman solve run only on rebalance events.
Forced rebalances
Two events can trigger a solve outside the normal schedule:
The regime filter changes from CASH back to ACTIVE.
The number of assets with sufficient history changes.
This prevents the portfolio from waiting many bars before responding to a material change in state.
Regime filter
The script includes an optional regime filter based on the chart symbol.
The filter compares:
A fast EMA.
A slow EMA.
When the fast EMA is above the slow EMA:
Regime = ACTIVE
When the fast EMA is not above the slow EMA:
Regime = CASH
This filter applies to the chart symbol , not individually to the fifteen assets.
That distinction is important.
If the indicator is placed on SPX, the regime filter reflects SPX.
If it is placed on Bitcoin, it reflects Bitcoin.
The regime state therefore acts as a global risk-on/risk-off switch for the entire portfolio.
CASH regime
When the regime filter turns off:
The live asset weights are flattened to zero.
The strategy stops compounding asset returns while the regime remains inactive.
When the filter turns ACTIVE again:
A new Black-Litterman solve is forced immediately.
The user should therefore choose the chart symbol intentionally if the regime filter is enabled.
Regime filter limitation
A single chart-symbol EMA regime is an intentionally simple overlay on a much more sophisticated cross-asset model.
It should not be confused with a multi-asset economic-regime model.
It answers only:
Is the fast trend of the chart symbol above its slower trend?
The regime layer can have a very large impact on historical results.
Backtests with and without it are therefore testing materially different systems.
Transaction costs
The script calculates turnover on each committed rebalance:
Turnover = Sum of |New Weight - Previous Weight|
The selected transaction-fee rate is then applied to that turnover.
This is more realistic than assuming rebalancing is free.
However, the cost model remains simplified.
It does not separately model:
Bid-ask spread.
Slippage.
Market impact.
Short borrow fees.
Financing costs.
Taxes.
Different fee schedules by asset.
The fee input should therefore be treated as an approximate portfolio-level trading-cost assumption.
Important backtest implementation note
The current implementation charges transaction fees when a new active portfolio is committed during a rebalance.
The transition that flattens the portfolio when the regime filter enters CASH is not separately charged an explicit turnover fee in the current code.
Therefore, backtests using the regime filter may slightly understate transaction costs associated with risk-off exits.
This is one reason the script should be treated as a concept rather than a production execution simulator.
No-lookahead portfolio return handling
The portfolio return for the current bar is calculated using the weights that were already active before the current rebalance solve.
Only after that return has been calculated does a new set of weights become active.
This prevents the optimizer from using newly calculated current-bar weights to capture a return that occurred before those weights could have existed.
This ordering is essential for a meaningful historical simulation.
Prior versus posterior weight chart
One of the main visual components is the paired horizontal weight chart.
Each asset receives two bars:
Prior weight.
Final active portfolio weight.
The prior represents the selected equilibrium starting allocation.
The active portfolio reflects the portfolio after:
Views.
Optimization.
Short constraints.
Gross normalization.
Volatility targeting.
Position caps.
Final gross caps.
Therefore, the visible gap between the bars represents more than the mathematical Black-Litterman posterior alone.
It represents the complete practical allocation change from prior to final active book .
If the regime filter is currently in CASH, the live active weights may be zero.
This distinction is important when interpreting the chart.
Allocation table
The Allocation Table shows each of the fifteen assets with:
Prior Weight.
Post Weight.
Delta Weight.
Equilibrium Expected Return.
Posterior Expected Return.
Prior Weight
The allocation before investor views and final portfolio construction.
Post Weight
The current active portfolio weight after the complete optimization and risk-control process.
Delta Weight
The difference between the active weight and prior weight.
Positive values indicate the asset has been increased relative to the prior.
Negative values indicate it has been reduced.
Equilibrium E
The implied return derived through reverse optimization.
Posterior E
The expected return after the active investor views have been incorporated.
Comparing equilibrium and posterior expected return is often more informative than looking only at weights.
A return expectation can change substantially while the final weight changes only modestly because:
The asset is highly volatile.
It is highly correlated with another holding.
The maximum-weight constraint binds.
Portfolio volatility limits exposure.
Views table
The Views Table shows each active view and includes:
View description.
Q.
Confidence.
Omega.
Q - PΠ.
This allows the user to inspect not only what the view says, but how strongly it conflicts with equilibrium and how uncertain it is.
Two views with identical Q values may have very different portfolio effects if:
Confidence differs.
Covariance differs.
Equilibrium expectations differ.
Current Book table
The Current Book table provides a compact summary of the active portfolio.
It includes:
ACTIVE or CASH regime.
Prior scheme.
Number of active views.
Number of rebalances.
Gross exposure.
Net exposure.
Number of live assets.
Turnover.
Risk-aversion Delta.
Tau.
Estimated portfolio volatility.
Volatility scaling factor.
This table is useful for diagnosing why the allocator currently looks the way it does.
For example:
Large view changes but small weights
may be explained by a tight volatility target or maximum-weight constraint.
Large gross but low net
may indicate significant long-short exposure.
Few live assets
means part of the universe has not yet accumulated sufficient historical data.
Equity curve
The script maintains a simulated portfolio equity curve beginning from the selected Initial Capital.
Initial Capital affects only the scale of the equity curve.
It does not affect:
Weights.
Sharpe ratio.
Volatility.
Portfolio optimization.
The equity curve compounds the historical portfolio returns generated by the active weights.
The line changes colour according to whether equity increased or decreased from the previous bar.
Benchmark Buy & Hold
A benchmark equity curve can be displayed beside the portfolio.
Both curves begin from the same nominal capital.
The benchmark is also used in:
Beta.
Alpha.
The benchmark can be changed independently from the fifteen-asset universe.
For meaningful interpretation, the benchmark should be relevant to the portfolio being studied.
A broad global macro portfolio compared only with SPX is answering a different question from an equity portfolio compared with SPX.
Daily returns
The script can optionally plot the portfolio’s per-bar percentage return.
This is useful for visually inspecting:
Return clustering.
Large gains.
Large losses.
Regime-filter cash periods.
Because it shares the pane with the equity curve, it is generally best viewed separately.
Rolling drawdown
Drawdown is measured relative to the previous portfolio-equity peak:
Drawdown = (Current Equity - Peak Equity) / Peak Equity
The result is negative while the portfolio remains below its historical high.
The visual fill becomes stronger as drawdown deepens.
The Max DD for Scaling input affects only the visual intensity scale.
It does not limit portfolio losses or modify the allocation.
Performance metrics
The metrics table includes a broad range of return and risk statistics.
Net Profit
Percentage change in portfolio equity from initial capital.
Maximum Drawdown
Largest historical peak-to-trough decline in the simulated portfolio.
Win Rate
Percentage of non-zero portfolio-return bars that were positive.
Flat CASH bars are excluded from the win/loss count.
This prevents periods where the portfolio is deliberately inactive from automatically being classified as losing periods.
Annual Mean Return
Arithmetic average per-bar portfolio return multiplied by the selected annualization factor.
This is not identical to CAGR.
Annual Standard Deviation
Per-bar return standard deviation scaled by the square root of the annualization factor.
Variance
Square of annualized standard deviation.
Sharpe Ratio
Measures annualized excess mean return relative to total return volatility using the selected risk-free rate.
Sortino Ratio
Measures return relative to downside-return variability rather than total volatility.
Omega Ratio
Compares the aggregate positive portfolio returns with the magnitude of aggregate negative portfolio returns.
Gain-to-Pain
Compares net return with the aggregate magnitude of negative returns.
CAGR
Compound annual growth rate based on beginning equity, ending equity and elapsed calendar time.
Calmar Ratio
CAGR divided by absolute maximum drawdown.
Beta
Measures covariance of portfolio returns with benchmark returns relative to benchmark variance.
Alpha
Estimates annualized portfolio return in excess of the return implied by its benchmark Beta and selected risk-free rate.
Skewness
Measures asymmetry of the historical portfolio-return distribution.
Positive skew indicates a longer or heavier positive tail.
Negative skew indicates a more pronounced negative tail.
VaR 95th Percentile
The implementation reports the fifth percentile of historical portfolio returns.
It can be interpreted as the lower-tail return threshold associated with approximately the worst 5% of observations.
It is displayed as a return value rather than converting the loss into a positive number.
Conditional VaR
Conditional VaR averages the returns in the lowest 5% tail.
This provides information about the average severity of outcomes beyond the VaR threshold.
Historical VaR and Conditional VaR rely entirely on the observed backtest sample.
They should not be interpreted as guarantees about future tail losses.
Risk-free rate
The selected Risk-Free Rate influences:
Sharpe.
Alpha.
Auto risk-aversion estimation.
Changing it therefore affects both reported performance statistics and potentially the portfolio itself when Auto Delta is enabled.
Understanding prior versus posterior
The most important conceptual visualization in the script is the difference between the prior and posterior state.
Suppose the prior allocation is:
Asset A: 20%
Asset B: 20%
Asset C: 20%
Asset D: 20%
Asset E: 20%
Now suppose the investor enters:
Asset A will outperform Asset B by 8%, with high confidence.
Black-Litterman does not simply add 8% weight to A and remove 8% from B.
Instead, the model asks:
What did equilibrium already imply about A versus B?
How uncertain is the prior?
How confident is the investor?
What is the covariance of the A-minus-B view?
How are A and B related to the rest of the portfolio?
The resulting posterior return adjustment then passes through the optimizer.
The final weights are subsequently modified by the portfolio constraints.
This explains why Black-Litterman allocations can behave very differently from manually applying arbitrary portfolio tilts.
Example: low-confidence relative view
Suppose equilibrium implies:
Expected A return = 8%
Expected B return = 7%
The equilibrium difference is 1%.
The investor believes:
A will outperform B by 5%
but assigns only 20% confidence.
The view disagrees with equilibrium, but Omega is relatively large because confidence is low.
The posterior therefore moves toward the investor view without fully accepting it.
Example: high-confidence relative view
Using the same equilibrium assumptions, suppose confidence is increased to 90%.
Omega becomes much smaller.
The investor view therefore carries much greater influence.
The posterior A-minus-B expected-return spread moves much closer toward the stated view.
The final weights may then shift significantly, subject to risk and portfolio constraints.
Example: view already priced into equilibrium
Suppose the user believes A will outperform B by 5%.
But the equilibrium prior already implies approximately 5%.
Then:
Q - PΠ ≈ 0
There is little disagreement to resolve.
Even a high-confidence view may produce only a small posterior adjustment.
This is an important property of the model.
Black-Litterman does not reward the user simply for entering a strong opinion.
The opinion must differ from equilibrium before it meaningfully changes the posterior.
Absolute versus relative confidence
Absolute views generally require greater confidence in the expected return level itself.
Relative views can be easier to interpret because the user only needs an opinion about the spread between two assets.
For example:
“Equities will return 14%.”
is a stronger forecasting statement than:
“Equities will outperform bonds by 4%.”
Neither is inherently superior.
The model supports both because portfolio managers frequently express views in both forms.
Why the model is useful conceptually
The value of Black-Litterman is not that it discovers the future.
It provides a disciplined method for converting beliefs into portfolio changes.
Without a framework, an investor may say:
“I like gold.”
“I am bearish equities.”
“Bitcoin should outperform bonds.”
but those statements do not specify:
How much the portfolio should change.
How volatility should affect the position.
How correlated assets should respond.
How conviction should change the allocation.
Black-Litterman forces those opinions into a structured portfolio context.
That is what this indicator is intended to demonstrate.
Important implementation difference from institutional Black-Litterman
The script implements the core Black-Litterman mechanics, but several choices are intentionally simplified for TradingView.
These include:
A fixed maximum universe of fifteen assets.
Up to five investor views.
User-selected fixed covariance shrinkage rather than automatically estimated shrinkage intensity.
Equal-weight and inverse-volatility priors in addition to manual market-style priors.
A simplified Auto Delta estimate.
Discrete bar-based rebalancing.
Simplified transaction costs.
A single chart-symbol regime filter.
Historical covariance from TradingView price data.
These choices make the model practical and interpretable inside Pine Script.
They also mean that results should not be compared directly with a production institutional implementation without understanding the differences.
Mixed-market data considerations
Cross-asset portfolios introduce data-alignment problems.
Cryptocurrency trades continuously.
Equities, commodities and bonds have market sessions and holidays.
Different TradingView symbols may also come from different exchanges or data providers.
The covariance matrix assumes the return observations are meaningfully aligned.
Users should therefore be careful with:
Intraday mixed-asset universes.
Assets from incompatible sessions.
Symbols with limited historical coverage.
Synthetic or non-tradable price series.
Daily or broader timeframes are generally easier to interpret for a macro allocation concept.
Backtest limitations
Historical simulation is useful for understanding behaviour, but this should not be treated as proof of future performance.
The backtest does not model every real-world implementation issue.
Examples include:
Bid-ask spreads.
Market impact.
Execution latency.
Portfolio financing.
Borrow availability.
Short borrow costs.
Taxes.
Different trading sessions.
Rebalancing at exact executable prices.
Changes in instrument availability.
Survivorship effects in a manually selected universe.
The model also uses historical covariance as an estimate of future covariance.
Correlations can change abruptly during stress periods.
The most diversified-looking portfolio based on historical data can become much more concentrated in risk when formerly independent assets begin moving together.
No automatic investment views
The script does not create investor views for the user.
Q and confidence are deliberately manual.
This is important because Black-Litterman is a framework for combining beliefs with equilibrium.
It does not tell the investor what those beliefs should be.
Views could theoretically come from:
Macro analysis.
Valuation models.
Momentum models.
Fundamental research.
Quantitative forecasts.
Discretionary judgement.
The quality of the posterior cannot exceed the quality of the assumptions provided to it.
Parameter interaction
Black-Litterman parameters should not be tuned independently.
Several important interactions exist.
Tau + Confidence
Both influence how aggressively views move the posterior.
Higher prior uncertainty combined with high view confidence can create strong posterior changes.
Covariance Lookback + Shrinkage
A short noisy covariance window may require more shrinkage for stability.
A long sample may tolerate less.
Target Volatility + Leverage Caps
A high volatility target may have little effect if maximum leverage or gross exposure is restrictive.
Views + Max Weight
A strong posterior preference for one asset may never appear fully in the active portfolio if the asset cap is binding.
Shorts + Gross Exposure
Allowing shorts can materially increase gross exposure even when net exposure looks conservative.
Rebalance Frequency + Fees
Frequent optimization allows faster adaptation but increases turnover and assumed trading cost.
Prior selection
The choice of prior is not cosmetic.
It changes the equilibrium return vector itself.
The same investor views can therefore produce different posterior portfolios depending on whether the starting prior is:
Equal Weight.
Inverse Volatility.
Market-like Manual Weights.
Users studying the framework should therefore treat prior construction as one of the primary model assumptions.
Suggested research workflow
A useful way to study the indicator is:
Begin with no investor views.
Choose a prior.
Observe the implied equilibrium returns.
Inspect the covariance-driven allocation.
Add one low-confidence relative view.
Observe Q - PΠ.
Compare equilibrium and posterior returns.
Increase confidence gradually.
Observe how the posterior and weights respond.
Add a second view.
Experiment with Tau.
Enable and disable posterior covariance.
Compare long-only and short-enabled portfolios.
Change the volatility target.
Observe when position or gross caps become binding.
This is generally more informative than immediately entering five aggressive views and trying to interpret the final result.
Example research questions
The allocator can be used to study questions such as:
How much does a 70% confidence view move the portfolio compared with 30% confidence?
How does inverse-volatility equilibrium differ from equal-weight equilibrium?
How does covariance shrinkage change portfolio concentration?
How do relative views propagate into assets not explicitly named?
How much does volatility targeting alter the raw optimizer?
How often do hard position caps bind?
How different are equilibrium expected returns from posterior expected returns?
How much turnover is generated by monthly versus weekly rebalancing?
How does a regime filter alter drawdown and opportunity cost?
These are the types of questions the concept is designed to explore.
Input guide
Initial Capital
Controls the starting dollar value of the simulated equity curve.
It does not change portfolio weights.
Trading Days/Year
Controls annualization.
Use a value consistent with the universe being studied.
Target Volatility
Sets the desired annualized portfolio-volatility target before hard leverage and weight constraints.
Transaction Fees
Approximate fee charged per unit of rebalance turnover.
Rebalance Every N Bars
Controls how frequently the full covariance and Black-Litterman solve occurs.
Allow Short Weights
Allows negative optimized weights.
Max Weight per Asset
Hard cap on individual position magnitude after volatility targeting.
Gross Exposure
Target absolute exposure before volatility scaling.
Max Gross After Vol Target
Final portfolio-level ceiling on gross exposure.
Max Vol-Target Leverage
Maximum scaling multiplier permitted by volatility targeting.
Covariance Lookback
Historical window used for covariance estimation and minimum data availability.
Covariance Shrinkage
Reduces off-diagonal covariance estimates toward zero.
Tau
Controls uncertainty in the equilibrium prior.
Use Posterior Covariance
Allows view uncertainty to modify the covariance matrix used by the optimizer.
Risk Aversion
Selects automatically estimated or manually specified Delta.
Prior Weight Scheme
Selects Equal Weight, Inverse Volatility or Manual Weights.
Investor Views
Supports up to five annualized absolute or relative return views.
Confidence
Controls the uncertainty assigned to each view.
Start Date
Defines the beginning of simulated portfolio equity.
Historical data before the date may still be used to warm up covariance estimates.
Risk-Free Rate
Used in portfolio statistics and Auto Delta estimation.
Benchmark
Used for the buy-and-hold comparison, Alpha and Beta.
Regime Filter
Optional chart-symbol fast/slow EMA filter that moves the portfolio between ACTIVE and CASH.
Prior vs Posterior visualization
Displays the difference between the selected prior allocation and current final portfolio weights.
Strengths
Implements the central Black-Litterman prior-and-views framework directly in Pine.
Supports both absolute and relative investor views.
Allows confidence to directly control view uncertainty.
Uses a complete cross-asset covariance matrix.
Includes diagonal covariance shrinkage.
Supports dynamic asset-data availability.
Provides equal-weight, inverse-volatility and manual priors.
Supports long-only and long-short allocation.
Uses covariance-aware portfolio volatility targeting.
Includes individual and portfolio-level exposure constraints.
Accounts for rebalance turnover fees.
Provides extensive allocation, view and portfolio diagnostics.
Includes a visual prior-versus-final-weight comparison.
Includes portfolio equity, benchmark and risk statistics.
Limitations
This is a concept and educational implementation, not an institutional portfolio-management system.
Historical covariance is only an estimate of future relationships.
The 15-asset universe is fixed in size.
A maximum of five views can be entered.
The prior is only a true market-equilibrium proxy if the selected weights appropriately represent one.
Equal Weight and Inverse Volatility are practical prior substitutes rather than literal global market-cap equilibrium.
The shrinkage coefficient is user-selected rather than statistically estimated.
Auto Delta is a practical approximation.
Portfolio optimization remains sensitive to inputs.
Poor views can produce poor posterior estimates.
High-confidence incorrect views can materially damage the portfolio.
Volatility targeting does not protect against all forms of risk.
Historical volatility can underestimate future crisis volatility.
Hard constraints mean the final portfolio may differ substantially from the analytical unconstrained Black-Litterman optimum.
The final volatility target may not be reached when position, leverage or gross limits bind.
The regime filter is based only on the chart symbol.
The backtest uses simplified transaction costs.
Regime-driven exits to CASH are not separately charged an explicit turnover fee in the current implementation.
Mixed-market TradingView data can contain differing sessions and histories.
Backtested performance does not establish future performance.
Historical and theoretical context
The Black-Litterman framework was developed to address practical problems encountered when applying mean-variance optimization to global portfolios.
Its central contribution is not simply another optimization equation.
It is a different way of constructing expected returns.
Instead of requiring the investor to estimate every asset’s return independently, equilibrium returns provide a coherent starting point. Investor views then alter only the parts of that equilibrium where the investor has an opinion.
This structure can be summarized as:
Start neutral.
Reverse-engineer equilibrium.
State where you disagree.
State how strongly you disagree.
Let covariance propagate those beliefs.
Re-optimize the portfolio.
The original Black-Litterman work emphasized equilibrium as a neutral starting point and allowed investor opinions about absolute or relative performance to tilt that equilibrium according to confidence.
Later work on user-specified confidence made the view-uncertainty problem easier to interpret by expressing conviction in intuitive percentage terms rather than requiring users to manually specify an abstract uncertainty covariance for every view.
This indicator takes those principles and translates them into a practical TradingView research environment.
Summary
Black-Litterman Allocator is an experimental portfolio-allocation framework designed to demonstrate how equilibrium, investor beliefs and portfolio risk can be combined inside TradingView.
The model begins with fifteen selectable assets and estimates their annualized covariance structure using historical log returns. A user-controlled shrinkage process reduces noisy cross-asset covariance estimates, while assets without sufficient historical data are excluded until a complete covariance window becomes available.
The user then selects an Equal Weight, Inverse Volatility or Manual prior portfolio.
That prior is reverse-optimized into implied equilibrium expected returns:
Pi = Delta × Sigma × Prior Weights
Up to five absolute or relative investor views can then be introduced.
Each view specifies:
What the investor expects.
Which assets the view applies to.
How confident the investor is.
Confidence is translated into view uncertainty, allowing weak opinions to create small tilts and high-confidence opinions to exert greater influence.
The Black-Litterman posterior combines those views with equilibrium while accounting for covariance relationships across the entire portfolio.
The resulting posterior expected returns are converted into an optimized allocation, after which the script applies:
Data-availability rules.
Optional long-only constraints.
Gross-exposure normalization.
Portfolio volatility targeting.
Maximum leverage.
Maximum position sizes.
Maximum gross exposure.
The portfolio is then rebalanced through time, transaction costs are approximated, an optional chart-level regime filter can move the book into CASH, and the resulting historical equity curve is compared with a selectable benchmark.
Extensive tables show:
Prior and final weights.
Equilibrium and posterior returns.
View confidence and uncertainty.
View disagreement with equilibrium.
Gross and net exposure.
Portfolio volatility.
Turnover.
Performance and risk statistics.
The purpose of the script is not to claim that Black-Litterman can identify the optimal future portfolio.
Its purpose is to make the framework tangible.
It provides a way to explore how a neutral portfolio can be translated into implied expected returns, how subjective beliefs can be incorporated without completely discarding that prior, how confidence changes the strength of those beliefs, how covariance spreads their effects across the portfolio, and how practical constraints can transform a theoretical posterior into a more realistic active allocation.
Treat the indicator as a concept, a research tool, and a visual implementation of portfolio-allocation theory rather than as an automated investment recommendation.
Indicador
Nonparametric Relative Momentum [BackQuant]Nonparametric Relative Momentum
Overview
Nonparametric Relative Momentum is a percentile-rank oscillator that measures where the current price or momentum observation sits relative to its own recent empirical history.
Unlike conventional momentum oscillators that transform price using fixed arithmetic relationships, this indicator uses rank statistics . The current observation is compared directly against the previous values in a rolling window and converted into a percentile score from 0 to 100.
The result answers a simple question:
How extreme is the current observation relative to what this market has actually done recently?
Two calculation modes are available:
Price ranks the selected price source directly.
Momentum first measures price change across a configurable horizon, then ranks that momentum against its own recent history.
The oscillator also includes:
Mid-rank handling for tied observations.
Optional output smoothing.
An EMA signal line.
Configurable overbought and oversold zones.
Stepped intensity colouring as the rank becomes more extreme.
Main-chart candle colouring from the 50 midline regime.
Alerts for midline, extreme-zone and signal-line crossings.
Why “nonparametric”?
In statistics, a parametric method generally assumes that data can be described by a particular distribution or by parameters associated with that distribution.
A nonparametric method does not require the same distributional assumption.
Percentile ranks are a classic example.
The oscillator does not need to assume that recent price changes are:
Normally distributed.
Symmetric.
Constant in volatility.
Characterised by a stable mean and standard deviation.
Instead, it works directly from the ordering of the observed data.
If the current momentum observation is greater than almost every momentum observation in the recent window, it receives a high rank.
If it is lower than almost everything observed recently, it receives a low rank.
This makes the oscillator fundamentally relative to the market’s own recent empirical distribution.
Core calculation
The calculation occurs in three stages:
Select the series to rank.
Calculate its empirical percentile rank.
Optionally smooth that rank and calculate a signal average.
The selected ranking target depends on the Rank Target input.
Price Mode
In Price mode:
Target = Selected Price Source
The current source value is compared with the previous values in the Rank Window.
This answers:
Where is current price positioned within its recent price distribution?
A value near 100 means current price is above almost every observation in the comparison window.
A value near 0 means it is below almost every observation.
A value near 50 means it sits near the middle of its recent distribution.
Because Price mode ranks the price level itself, it behaves somewhat like a stochastic or price-position oscillator, although the calculation is based on empirical ranking rather than highest-lowest range normalisation.
Momentum Mode
Momentum mode first calculates:
Momentum = Source - Source
This measures the absolute price change across the selected Momentum Length.
The resulting momentum series is then percentile-ranked over the Rank Window.
The oscillator therefore answers:
How strong is the current momentum observation compared with recent momentum observations?
This is different from asking whether price itself is historically high or low.
For example, price can be near a recent high while momentum has weakened considerably. In that situation:
Price mode may remain highly ranked.
Momentum mode may fall toward the centre or lower half of the distribution.
Conversely, price does not need to be at a long-term extreme for momentum to rank very highly if the current change is unusually strong relative to recent movements.
Why Momentum mode is different from traditional RSI
The standard Relative Strength Index developed by J. Welles Wilder compares smoothed positive and negative price changes.
Its calculation depends on the relative magnitude of average gains and average losses.
Nonparametric Relative Momentum does not use that formula.
Instead:
A momentum observation is calculated.
That observation is ranked against its own historical sample.
For this reason, Momentum mode can be thought of as a rank-based relative momentum oscillator .
Both traditional RSI and this oscillator are bounded between 0 and 100, but the meaning of those values is different.
For example:
RSI = 90
means the balance of smoothed gains versus losses has produced an RSI reading of 90.
Nonparametric Relative Momentum = 90
means the current momentum observation ranks around the upper end of its recent empirical momentum distribution.
That distinction is important.
Percentile rank calculation
For each bar, the indicator compares the current target with every observation in the preceding Rank Window.
It counts:
How many previous values are below the current value.
How many previous values are exactly equal to it.
The percentile rank is then:
Rank = 100 × (Values Below + 0.5 × Equal Values) / Window Length
This produces an oscillator between 0 and 100.
Why use rank instead of magnitude?
Consider two markets.
Market A may normally move only 0.5% over the selected momentum horizon.
Market B may routinely move 5%.
A raw momentum threshold cannot be interpreted the same way for both.
Ranking changes the question.
Instead of asking:
How many points or percent did this market move?
the oscillator asks:
How unusual is this move relative to this market’s own recent behaviour?
This allows the same 0–100 framework to adapt naturally to different price scales and volatility regimes.
Mid-rank treatment of ties
A simple percentile implementation might count only observations strictly below the current value.
That can distort the result when repeated values occur.
This indicator uses mid-rank treatment .
If historical observations equal the current value, each tie contributes one half rather than being classified entirely above or below.
For example, suppose:
40% of observations are below the current value.
20% are exactly equal.
40% are above.
The mid-rank result is:
40 + 0.5 × 20 = 50
This places the tied observation at the centre of its equal-value group.
Mid-ranks are commonly used in rank-based statistics because they provide a more balanced treatment of ties.
Rank Window
The Rank Window determines how much historical data defines the current empirical distribution.
A shorter Rank Window:
Adapts quickly.
Responds strongly to recent regime changes.
Produces more rapid movement between percentiles.
Can create noisier extreme readings.
A longer Rank Window:
Builds the ranking from a larger sample.
Produces a more stable percentile estimate.
Makes extremes harder to reach.
Responds more slowly when market behaviour changes.
The window therefore controls the memory of the oscillator.
It does not smooth the underlying target directly. It changes the reference distribution against which the target is ranked.
Momentum Length
Momentum Length is used only when Rank Target is set to Momentum.
It controls the horizon over which price change is measured:
Momentum = Current Source - Source from Momentum Length bars ago
Shorter values:
Measure faster momentum.
React to shorter impulses.
Change direction more frequently.
Longer values:
Measure broader displacement.
Focus on more persistent movement.
Ignore more short-term fluctuation.
The Momentum Length and Rank Window perform separate roles.
Momentum Length determines what movement is measured.
Rank Window determines the historical sample against which that movement is judged.
Output Smoothing
The raw percentile rank can optionally be passed through an EMA.
A value of 1 leaves the rank effectively unsmoothed.
Higher values:
Reduce rapid rank fluctuations.
Create a smoother oscillator.
Reduce short-lived extreme readings.
Introduce additional lag.
The smoothing occurs after the percentile calculation.
It does not change how observations are ranked.
The 50 midline
The oscillator is centred around 50.
A value above 50 means the current observation ranks above the midpoint of its recent distribution.
A value below 50 means it ranks below the midpoint.
The interpretation depends on the selected mode.
Price mode above 50
Current price is positioned in the upper half of its recent price distribution.
Price mode below 50
Current price is positioned in the lower half.
Momentum mode above 50
Current momentum is stronger than roughly the middle of its recent momentum observations.
Momentum mode below 50
Current momentum is weaker relative to its recent distribution.
The indicator also uses this midline to colour main-chart candles:
Above or equal to 50 = bullish colour.
Below 50 = bearish colour.
This provides a simple relative-regime view on the price chart.
Percentile extremes
Because the oscillator represents rank rather than an unbounded magnitude, readings near 0 and 100 carry a straightforward interpretation.
Near 100
The current observation is greater than almost every value in the recent comparison window.
Near 0
The current observation is lower than almost every value.
These are empirical extremes.
They do not mean price or momentum cannot become more extreme.
A value near 100 can persist while a strong trend continues because new observations may repeatedly remain near the top of the evolving distribution.
Likewise, readings near 0 can persist during sustained downside momentum.
Overbought and Oversold zones
The default static zones are:
Overbought: 90–100
Oversold: 0–10
These are configurable.
The labels “overbought” and “oversold” describe statistical location, not guaranteed reversal conditions.
An overbought reading means:
The ranked observation is near the top of its recent empirical distribution.
An oversold reading means:
It is near the bottom.
During a range, these areas may help identify local extremes.
During a persistent trend, the oscillator can remain in an extreme zone for extended periods.
The zones should therefore be interpreted together with:
Trend context.
Price structure.
Oscillator direction.
Signal-line behaviour.
Why 90/10 instead of 70/30?
Traditional RSI commonly uses 70 and 30.
That convention does not need to apply to a percentile-rank oscillator.
A rank above 90 means the current observation is in approximately the upper tail of the recent empirical sample, while a reading below 10 represents the lower tail.
Using more extreme default zones makes them intentionally selective.
Users who want broader zones can move the boundaries toward values such as 80 and 20.
Signal line
The white Moving Average line is an EMA of the final oscillator:
Signal = EMA(Percentile Rank Oscillator, Signal Length)
This provides a slower reference against which short-term rank movement can be compared.
Oscillator above signal
The percentile rank is strengthening relative to its own recent smoothed level.
Oscillator below signal
The rank is weakening.
Crossovers can be used to identify changes in short-term momentum within the broader percentile regime.
For example:
A bullish crossover below the oversold zone can indicate rank beginning to recover from an extreme.
A bearish crossover above the overbought zone can indicate deterioration from an upper-tail reading.
A crossover near 50 may represent a more neutral momentum transition.
Signal crosses should not be interpreted independently from oscillator location.
Stepped oscillator colouring
The oscillator uses stepped colour intensity based on its position relative to the 50 midline.
Above 50, colours progressively strengthen as the percentile reaches higher levels.
Below 50, bearish intensity progressively strengthens as the percentile falls.
The main regions are approximately:
50–62.5: modest positive rank.
62.5–75: strengthening positive rank.
75–90: strong positive rank.
90–99: upper-tail extreme.
99–100: exceptional upper-tail rank.
The lower half mirrors this concept:
37.5–50: modest negative rank.
25–37.5: weakening relative state.
10–25: strong negative rank.
1–10: lower-tail extreme.
0–1: exceptional lower-tail rank.
These colours do not introduce additional calculations or signals.
They visually communicate how far the oscillator has moved into its empirical distribution.
Column presentation
The percentile oscillator is plotted as columns around a histogram base of 50.
This means:
Values above 50 extend upward.
Values below 50 extend downward from the midline.
Although the numerical scale remains 0–100, this presentation visually emphasises deviation from the centre of the distribution.
The 50 level therefore functions as the oscillator’s equilibrium reference.
Price mode versus Momentum mode
The two modes answer different questions and should not be treated interchangeably.
Price Mode
Asks:
Where is price relative to its recent distribution?
This makes it useful for:
Range position.
Breakout context.
Relative price extremes.
Stochastic-like analysis.
Momentum Mode
Asks:
Where is current price change relative to the recent distribution of price changes?
This makes it useful for:
Momentum expansion.
Momentum exhaustion.
Relative impulse analysis.
Trend-strength transitions.
Momentum mode can identify weakening momentum before price itself leaves the upper part of its distribution.
Price mode can remain elevated simply because the market is still trading near recent highs.
Example: strong uptrend
Suppose price has been rising steadily.
Price Mode may remain above 90 because current price continually sits near the upper edge of its recent range.
Momentum Mode may behave differently:
It can rise toward 100 during acceleration.
Fall back toward 50 when the trend continues at a more ordinary pace.
Drop below 50 if momentum deteriorates significantly even while price remains relatively high.
This distinction can help separate price location from momentum condition .
Example: volatility regime change
Suppose a market normally changes by only small amounts, then suddenly produces a large directional move.
Raw momentum alone shows a large number.
The percentile rank provides additional context by showing whether that movement is unusual relative to the recent distribution.
If the current momentum is greater than nearly every recent observation, the oscillator moves toward 100.
If the market has already experienced many similarly large moves, the same absolute momentum may receive a much less extreme rank.
The indicator therefore adapts automatically to changing empirical behaviour without requiring fixed momentum thresholds.
Midline crossings
A crossover above 50 indicates the ranked series has moved into the upper half of its recent distribution.
A cross below 50 indicates movement into the lower half.
In Momentum mode, these crossings can be used as a simple relative momentum regime:
Above 50 = comparatively stronger momentum state.
Below 50 = comparatively weaker momentum state.
In Price mode, they indicate whether price is above or below the central portion of its recent rank distribution.
These crossings also control the optional main-chart candle colours.
Extreme-zone crossings
The indicator provides alerts when:
The oscillator crosses upward into the overbought zone.
The oscillator crosses downward into the oversold zone.
These alerts identify entry into an extreme percentile area.
They do not indicate that the extreme has ended.
For reversal-oriented analysis, a trader may instead monitor:
A subsequent exit from the zone.
A signal-line crossover.
Divergence with price.
A break in market structure.
Divergence interpretation
Because Momentum mode ranks momentum rather than price, it can also be useful for examining momentum divergence.
For example:
Price may make a higher high while the oscillator produces a lower percentile peak.
This indicates that the latest momentum observation is less exceptional relative to its recent history than it was during the previous price high.
The reverse can occur at lows.
As with conventional divergence, this is evidence of changing momentum characteristics, not confirmation that price must reverse.
How to use the indicator
1. Relative momentum regime
In Momentum mode, use the 50 midline as a simple regime reference:
Above 50 = positive relative momentum state.
Below 50 = negative relative momentum state.
2. Momentum extremes
Use the configurable zones to identify unusually high or low momentum ranks.
Rather than automatically fading these conditions, determine whether the market is:
Trending.
Exhausting.
Breaking out.
Returning toward equilibrium.
3. Signal-line transitions
Oscillator and signal-line crosses can help identify shorter-term changes in rank direction.
The location of the crossover matters.
A bullish crossover at 5 carries different context from one at 95.
4. Price-distribution analysis
Switch to Price mode when the objective is to measure where the current market sits within its recent price distribution.
This can be useful for:
Breakout analysis.
Range positioning.
Relative high/low detection.
5. Trend confirmation
Momentum remaining consistently above 50 can support an existing bullish trend.
Momentum remaining below 50 can support a bearish trend.
Repeated oscillation around 50 indicates that relative momentum is changing sides frequently.
6. Candle regime colouring
The optional overlay candles make the oscillator’s midline state visible directly on the main price chart.
This can be useful when the oscillator pane is being used primarily for extremes and signal-line analysis.
Input guide
Rank Target
Selects what is percentile-ranked.
Price ranks the source itself.
Momentum ranks its change over the selected Momentum Length.
Rank Window
Controls the empirical comparison sample.
Longer values are smoother and statistically broader. Shorter values adapt more quickly.
Momentum Length
Controls the displacement horizon in Momentum mode.
It has no effect in Price mode.
Output Smoothing
Applies optional EMA smoothing to the percentile rank.
1 produces the raw rank.
Signal Length
Controls the EMA signal line.
Shorter values follow the oscillator more closely. Longer values produce slower crossover signals.
Overbought Zone
Sets the lower boundary of the upper extreme area.
Oversold Zone
Sets the upper boundary of the lower extreme area.
How this differs from RSI
Traditional RSI:
Separates gains and losses.
Smooths their magnitude.
Calculates a relative-strength ratio.
Transforms that ratio onto a 0–100 scale.
Nonparametric Relative Momentum:
Calculates price or momentum directly.
Ranks the current observation against historical observations.
Uses no gain/loss ratio.
Uses no assumed distribution.
The identical 0–100 scale therefore represents a different statistical concept.
How this differs from Stochastic
A conventional stochastic oscillator measures where current price lies between the highest high and lowest low of a window.
Its basic concept is:
(Current - Lowest) / (Highest - Lowest)
Nonparametric Price mode instead asks how many historical observations are below the current price.
This distinction matters because the rank considers the entire empirical ordering of the sample, not only its two extreme endpoints.
Two windows can have identical highs, lows and current price but different internal distributions.
A stochastic calculation can return the same value in both cases, while percentile rank can differ because the number of observations above and below the current price is different.
How this differs from a Z-score
A Z-score measures deviation from a mean in standard-deviation units:
Z = (Current Value - Mean) / Standard Deviation
That calculation depends directly on the sample mean and dispersion.
Percentile rank depends only on ordering.
As a result, an extreme outlier can heavily alter a mean and standard deviation but has much less influence on the ordering of the remaining observations.
This is one of the reasons rank statistics can be useful when financial data contains skew, fat tails or isolated extreme moves.
Strengths
Uses a nonparametric empirical ranking process.
Requires no assumption of normality.
Produces an intuitive bounded 0–100 scale.
Adapts naturally to the recent behaviour of each market.
Supports both price-location and momentum-ranking modes.
Uses mid-ranks for tied observations.
Normalises momentum extremes without relying on fixed point or percentage thresholds.
Includes configurable smoothing and signal analysis.
Provides direct midline regime colouring on the main chart.
Limitations
A percentile rank measures relative position, not absolute magnitude.
A reading of 100 does not indicate how much larger the current observation is than the rest of the sample.
Persistent trends can remain at extreme ranks for extended periods.
Short Rank Windows can generate rapid percentile changes.
Long Rank Windows adapt more slowly to regime shifts.
Momentum mode uses absolute source change rather than percentage return, although ranking substantially reduces scale dependence within a single instrument.
Extreme readings are not automatic reversal signals.
Signal-line crosses can whipsaw in noisy conditions.
The oscillator is reactive and does not forecast future price.
Alerts
The indicator provides alerts for:
Cross Up 50: oscillator enters the upper half of its distribution.
Cross Down 50: oscillator enters the lower half.
Overbought: oscillator crosses upward through the selected upper-zone boundary.
Oversold: oscillator crosses downward through the selected lower-zone boundary.
Bull: oscillator crosses above its signal EMA.
Bear: oscillator crosses below its signal EMA.
Summary
Nonparametric Relative Momentum converts either price or momentum into an empirical percentile rank.
Instead of asking how far an observation is from a moving average, how many standard deviations it sits from a mean, or what ratio of gains to losses produced it, the indicator asks where that observation ranks relative to its own recent history.
In Price mode, it measures the relative location of price within its historical distribution.
In Momentum mode, it first calculates price displacement across a chosen horizon and then measures how exceptional that momentum is relative to recent momentum observations.
A mid-rank procedure handles tied values, optional EMA smoothing controls visual responsiveness, and a separate signal average provides crossover analysis. The 50 midline separates the upper and lower halves of the empirical distribution, while configurable overbought and oversold zones highlight the tails.
The result is a distribution-free relative momentum framework that adapts to the observed behaviour of the market rather than relying on fixed magnitude thresholds or an assumed statistical distribution.
Indicador
Adaptive Trend Ensemble [BackQuant]Adaptive Trend Ensemble
Overview
Adaptive Trend Ensemble is an online-learning trend filter that combines eight different moving-average methods into one continuously weighted trend estimate.
Instead of selecting one moving average permanently, the indicator treats each method as an independent forecasting expert. Every bar, each expert is evaluated according to whether its previous slope correctly anticipated the direction of the latest price move.
Experts that were directionally correct retain more influence. Experts that were wrong lose influence through a multiplicative penalty. The weights are then normalised and used to blend all eight moving-average values into one adaptive ensemble line.
The indicator therefore attempts to answer two separate questions:
Which smoothing method has recently aligned best with price direction?*
How strongly do the weighted methods currently agree on the direction of trend?
The final output includes:
A dynamically weighted ensemble trend line.
Bullish and bearish trend-state colouring.
A gradient between price and the ensemble.
A consensus-driven glow.
Trend-coloured candles.
A live label showing the leading expert and its current weight.
Alerts when the ensemble trend changes direction.
This is not a fixed moving average and it is not a simple average of several indicators. The contribution of each expert changes over time according to its recent directional performance.
Core idea
Moving averages respond differently to the same market.
A Hull Moving Average may respond quickly during a sharp transition, while an RMA may remain stable through temporary noise. A linear-regression estimate may follow a smooth directional move well, while a conventional EMA may perform better during a more ordinary trend.
No individual smoothing method is consistently superior across every environment.
Markets alternate between:
Persistent trends.
Fast breakouts.
Slow directional drift.
Volatile reversals.
Compressed ranges.
Noisy transitions.
A fixed indicator cannot change its mathematical personality when the environment changes. It continues using the same weighting structure regardless of whether that structure currently suits the market.
Adaptive Trend Ensemble addresses this by maintaining a bank of different smoothing methods and changing their influence through time.
The model does not attempt to decide in advance which method is best. It allows recent realised price action to determine which experts should currently receive more weight.
Prediction with expert advice
The indicator is based on a class of online-learning methods commonly described as:
Prediction with Expert Advice
In this framework:
Several experts produce predictions.
The actual outcome is observed.
Each expert receives a loss based on its prediction.
Expert weights are updated.
The combined model places more influence on better-performing experts.
The term “expert” does not imply that each method is intelligent by itself. An expert is simply an individual forecasting rule.
In this indicator, the eight experts are eight moving-average methods.
The model uses a multiplicative-weights process closely related to the Hedge and Weighted Majority families of online-learning algorithms.
The central principle is:
Do not commit permanently to one model.
Track several models simultaneously.
Reduce the weight of models that make mistakes.
Allow the combined forecast to adapt as relative performance changes.
Online learning
The model learns sequentially, one bar at a time.
It does not train on a separate historical dataset and then freeze its parameters.
At each new bar:
The previous slope of each moving average is treated as that expert's prediction.
The realised close-to-close direction is observed.
Each expert receives a loss.
Weights are updated multiplicatively.
Weights are normalised.
The current expert values are blended using the new weights.
This makes the process online and adaptive.
The weight state is carried forward from bar to bar, meaning the current ensemble reflects the accumulated results of earlier expert decisions.
The expert bank
The ensemble contains eight moving-average experts:
Simple Moving Average - SMA*
Exponential Moving Average - EMA
Weighted Moving Average - WMA*
Hull Moving Average - HMA
Double Exponential Moving Average - DEMA*
Running Moving Average - RMA
Arnaud Legoux Moving Average - ALMA*
Least-Squares Moving Average - LSMA
All experts use the same Base Length.
This is important because it keeps their nominal observation horizon comparable. The ensemble is comparing different mathematical treatments of approximately the same lookback rather than comparing completely unrelated time horizons.
Even with an identical length, the experts behave differently because they assign weight to historical observations in different ways.
Simple Moving Average - SMA
The SMA applies equal weight to every observation inside the selected window.
Its general form is:
SMA = Sum of observations / Number of observations
The SMA is stable and easy to interpret, but every included observation has the same importance.
This can make it slower to react when a new trend begins because older prices continue to influence the average until they leave the window.
Within the ensemble, the SMA acts as a neutral equal-weight baseline.
Exponential Moving Average - EMA
The EMA assigns progressively greater weight to recent observations.
Its recursive form is based on:
EMA = α × Current Price + (1 - α) × Previous EMA
where α is determined by the selected length.
Compared with an SMA of the same length, an EMA generally responds more quickly to recent movement.
Its recursive weighting makes it useful during ordinary directional markets, although it can still turn repeatedly when price oscillates in a range.
Weighted Moving Average - WMA
The WMA assigns linearly increasing weight to more recent observations.
For example, in a simplified four-period WMA, the newest value receives four units of weight, while the oldest receives one.
This makes the WMA more responsive than an equal-weight SMA while retaining a finite lookback window.
Within the ensemble, it provides a direct recency-weighted alternative to the exponential behaviour of the EMA.
Hull Moving Average - HMA
The Hull Moving Average was designed to reduce lag while preserving a relatively smooth output.
Its construction combines weighted moving averages over different horizons, applies a lag-compensation step, and then smooths the result over approximately the square root of the original length.
Conceptually:
Calculate a faster WMA.
Calculate a slower WMA.
Use their difference to compensate for lag.
Smooth the compensated result.
The HMA often reacts quickly to changes in trend direction.
That responsiveness can make it valuable during strong transitions, but it may also make it more sensitive to short-term oscillation.
Double Exponential Moving Average - DEMA
Despite its name, DEMA is not simply an EMA calculated twice.
Its general construction is:
DEMA = 2 × EMA - EMA of EMA
The second EMA estimates some of the lag in the first EMA. Subtracting it attempts to create a smoother with less delay.
DEMA can respond quickly to directional changes, although reduced lag may also increase sensitivity during unstable conditions.
Running Moving Average - RMA
RMA is commonly associated with Wilder-style smoothing.
It uses a slower recursive update than a typical EMA of the same nominal length.
Its general form places substantial influence on the previous RMA value, producing a persistent and stable estimate.
The RMA expert often changes direction less aggressively than the faster methods.
Within the ensemble, it acts as one of the more conservative smoothing models.
Arnaud Legoux Moving Average - ALMA
ALMA applies a Gaussian-style weighting curve across the observation window.
The weighting distribution can be shifted toward more recent observations while maintaining a smooth bell-shaped profile.
The script uses a recent-weighted offset and a fixed Gaussian width.
ALMA attempts to balance:
Smoothness.
Reduced lag.
Controlled weighting of the observation window.
It provides a different weighting structure from the linear, exponential and lag-compensated experts.
Least-Squares Moving Average - LSMA
The LSMA is based on linear regression.
Instead of averaging historical prices directly, it fits a straight line through the selected window and evaluates the regression estimate at the current bar.
The method attempts to represent the local directional path of price.
LSMA can follow smooth trends closely because it models slope explicitly. However, it may respond strongly when the local regression direction changes abruptly.
Within the indicator, the LSMA is produced using the rolling linear-regression output.
Base Length
The Base Length is shared by all eight experts.
Lower values:
Make every expert more responsive.
Increase sensitivity to short-term changes.
Produce faster weight and trend changes.
Increase the possibility of whipsaws.
Higher values:
Create smoother expert outputs.
Focus the ensemble on broader trend structure.
Reduce short-term changes.
Increase lag during sudden reversals.
Because all experts share the same length, changing this setting adjusts the entire ensemble horizon.
It does not change the number of experts or their relative starting weights.
Expert predictions
The model evaluates each expert using the direction of its slope.
For each moving average:
Rising slope is represented as +1.
Falling or non-rising slope is represented as -1.
To evaluate the latest completed move, the script uses the expert's slope from the previous bar.
For example:
If the expert was rising from two bars ago to the previous bar, it predicted a positive current move.
If the expert was falling, it predicted a negative current move.
The realised outcome is determined from the current close relative to the previous close:
Close above previous close = positive realised direction.
Close below previous close = negative realised direction.
Unchanged close = zero realised direction.
The model therefore scores directional slope prediction, not the numerical distance between each moving average and price.
An expert is rewarded for getting direction right, even if its plotted value is relatively far from the market.
Likewise, an expert is penalised for getting direction wrong even if its line remains visually close to price.
Loss functions
The indicator provides two loss functions:
Directional 0/1*
Magnitude-weighted
The selected loss determines how strongly incorrect experts are penalised.
Correct experts receive zero loss under both modes.
Directional 0/1 loss
Directional mode treats every incorrect prediction equally.
The loss is:
0 when the expert predicted the realised direction correctly.
1 when the expert predicted incorrectly.
This means that an incorrect prediction on a very small move receives the same loss as an incorrect prediction on a large move.
Directional mode answers a simple question:
Was the expert right or wrong?
It does not consider how important the move was.
This mode can produce consistent learning because every directional observation is treated equally, but it may respond to small and insignificant price changes as strongly as major moves.
Magnitude-weighted loss
Magnitude-weighted mode scales the penalty according to the size of the realised move.
The move is normalised using ATR:
Move = Absolute close-to-close change / ATR
The ATR uses the shared Base Length.
The incorrect expert's loss becomes:
Loss = Normalised Move
with the magnitude capped at 3.
The cap prevents a single extreme bar from creating an unlimited penalty.
This mode gives greater importance to mistakes during large movements.
For example:
An incorrect expert during a 0.10 ATR move receives a small penalty.
An incorrect expert during a 1.00 ATR move receives a larger penalty.
An incorrect expert during a move above 3 ATR receives the capped penalty of 3.
Magnitude-weighted mode answers:
How costly was the directional mistake relative to current volatility?
This can make the ensemble adapt more strongly after significant movements while paying less attention to small fluctuations.
Flat price bars
If the current close is unchanged from the previous close, the realised direction is zero.
Because expert directions are encoded as either positive or negative, no expert can exactly match a zero realised direction.
Under Directional mode, all experts receive the same incorrect classification.
Because every weight is multiplied by the same penalty factor, their relative weight distribution remains effectively unchanged after normalisation.
Under Magnitude-weighted mode, the realised move is zero, so the resulting penalty is also zero.
In both cases, a completely flat close-to-close bar does not materially change the relative ranking of the experts.
Multiplicative weight update
Each expert begins with an equal weight:
Initial Weight = 1 / 8
After the loss is calculated, the weight is updated using:
New Unnormalised Weight = Old Weight × exp(-η × Loss)
where η is the Learning Rate.
This is the central Hedge or multiplicative-weights update.
Correct experts have zero loss:
exp(-η × 0) = 1
Their unnormalised weight is unchanged.
Incorrect experts have a positive loss, so their weight is multiplied by a value below one.
For example, in Directional mode with a Learning Rate of 2:
Incorrect Weight Multiplier = exp(-2) ≈ 0.135
An incorrect expert retains only about 13.5% of its previous unnormalised weight before the weight set is normalised again.
This does not mean its final displayed weight will necessarily fall by exactly 86.5%, because all expert weights are subsequently rescaled so they sum to one.
Why multiplicative updates are used
An additive system might subtract a fixed quantity from each incorrect expert.
That can create problems:
Weights can become negative.
The same penalty has a different effect on large and small weights.
The model may not adapt proportionally.
A multiplicative update preserves non-negative weights and penalises experts proportionally to their current influence.
It also allows the distribution to become concentrated around consistently successful methods.
Learning Rate - η
The Learning Rate controls how aggressively the ensemble shifts weight after mistakes.
Higher values:
Penalise incorrect experts more strongly.
Move influence rapidly toward recent winners.
Can produce winner-take-all behaviour.
Can make the leader change abruptly after a few important bars.
Lower values:
Produce gradual weight changes.
Keep the expert distribution more diversified.
Reduce sensitivity to short-term performance.
Make the model slower to adapt.
The Learning Rate does not change the moving averages themselves. It changes only how quickly their relative influence evolves.
High Learning Rate behaviour
At high settings, a wrong expert may lose most of its weight after one or two mistakes.
This can be beneficial when one smoothing method is clearly better suited to the current regime.
It can also create instability:
A recent winner can dominate the ensemble.
A temporary performance streak can cause excessive concentration.
The model can switch leaders quickly when conditions reverse.
Low Learning Rate behaviour
At low settings, the ensemble behaves more like a slowly adapting average of the expert bank.
No single observation dramatically changes the distribution.
This produces smoother adaptation, but a poorly suited expert may retain substantial influence for longer.
Weight normalisation
After all expert weights are updated, they are normalised:
Normalised Weight = Expert Weight / Sum of All Expert Weights
This ensures that the complete weight set sums to one.
The weights can then be interpreted as each expert's share of the ensemble.
For example:
A 25% weight means that expert contributes one quarter of the weighted output.
A 5% weight means its current influence is relatively small.
The weights are not probabilities that the experts will be correct on the next bar.
They are adaptive influence coefficients based on accumulated relative loss.
Weight Floor
The optional Weight Floor preserves a minimum allocation for every expert.
After normalisation, the adjusted weight is calculated so that:
Every expert receives at least the selected floor.
The remaining weight is distributed according to the normalised Hedge weights.
The full set continues to sum to one.
For eight experts, a floor of 0.01 reserves at least 1% for each expert.
This assigns:
A minimum combined mass of 8%.
The remaining 92% according to relative performance.
A floor of 0.05 reserves at least 5% for each of the eight experts, using 40% of the total distribution as minimum allocations.
The remaining 60% is distributed according to current performance.
Why use a floor?
Without a floor, repeatedly incorrect experts can approach a weight extremely close to zero.
Because the update only reduces weights after losses, an expert with almost no weight may require a long period of relative outperformance before it becomes influential again.
A positive floor keeps all methods alive.
This allows an expert that performed poorly in the previous regime to recover more quickly when the market environment changes.
Weight Floor set to zero
With a zero floor:
The model is free to concentrate almost entirely in one expert.
Recent winners can dominate strongly.
The ensemble can become highly specialised.
This produces the purest multiplicative-weights behaviour but increases the risk of weight collapse.
Positive Weight Floor
With a positive floor:
The expert bank remains diversified.
Cold experts retain some influence.
The model can recover more easily after regime changes.
The leading expert's maximum possible weight is reduced.
The floor therefore controls the balance between specialisation and diversity.
Ensemble output
After the weight update, the current values of the eight experts are blended:
Ensemble = Sum of Expert Weight × Expert Value
This is a weighted average in which the weights are determined by online directional performance.
If the HMA currently has the greatest weight, the ensemble will behave more like the HMA.
If the RMA and SMA dominate, the output will become smoother and more conservative.
If the weights are distributed evenly, the line represents a broad blend of all eight methods.
The output can therefore change its effective smoothing behaviour without changing the user-selected Base Length.
Line Smoothing
The weighted ensemble may be passed through an optional EMA for visual smoothing.
A setting of 1 effectively disables this additional stage.
Higher settings:
Create a smoother displayed line.
Reduce small slope changes.
Delay bullish and bearish flips.
This smoothing is cosmetic in the sense that it occurs after the online expert weighting.
It does not affect:
Expert predictions.
Expert losses.
Weight updates.
Consensus.
Leader selection.
It does affect the final plotted line and the trend state derived from that line.
Trend state
Trend direction is determined from the slope of the smoothed ensemble line.
If the line is above its previous value, trend becomes bullish.
If the line is below its previous value, trend becomes bearish.
If the line is unchanged, the previous trend persists.
This creates a persistent two-state regime.
A bullish flip occurs when the trend changes from bearish to bullish.
A bearish flip occurs when it changes from bullish to bearish.
The trend state is based on the ensemble's slope, not on price crossing the ensemble.
Price may be above or below the line without immediately changing its direction.
Consensus calculation
The indicator calculates a separate weighted directional vote.
Each expert's current slope direction is multiplied by its current weight:
Weighted Vote = Sum of Weight × Direction
Because each direction is either +1 or -1 and the weights sum to one, the vote lies between -1 and +1.
Examples:
+1 means all meaningful weight is assigned to rising experts.
-1 means all meaningful weight is assigned to falling experts.
0 means bullish and bearish weighted influence is evenly balanced.
The displayed consensus strength is:
Consensus Strength = Absolute Value of Weighted Vote
This converts the result to a range from zero to one.
0% means the weighted expert bank is evenly divided.
100% means the weighted influence is entirely aligned in one direction.
Weighted consensus versus expert count
Consensus is not calculated by simply counting how many of the eight experts are rising.
An expert with a 40% weight contributes more than one with a 2% weight.
For example:
Five low-weight experts may be bullish.
Three high-weight experts may be bearish.
The final weighted vote can still be bearish.
This means consensus measures the agreement of the current weighted model, not the raw number of methods on each side.
With a zero Weight Floor, consensus may become very high when one expert dominates, even if several near-zero-weight experts disagree.
With a positive floor, disagreement from the remaining experts has more influence on the consensus value.
Consensus is not confidence
The consensus percentage should not be interpreted as a probability that the trend will continue.
It measures only the current alignment of weighted expert slopes.
High consensus means:
The influential experts point in the same direction.
It does not guarantee:
Future price continuation.
A profitable entry.
Low reversal risk.
Strong agreement can occur late in a mature trend as well as early in a new one.
Leading method
The live information label identifies the expert with the highest current weight.
It displays:
The expert name.
Its current percentage weight.
The weighted consensus strength.
The current ensemble direction.
For example:
Leading: HMA (34.5%)*
Consensus: 78% ▲
This means the HMA currently has the largest share of the ensemble and the weighted expert bank is strongly aligned upward.
The leader percentage is not a win probability.
It is only the experts share of the current normalised weight distribution.
Leader changes
The leading method can change when:
The current leader makes directional mistakes.
Another expert remains correct while competitors are penalised.
A large magnitude-weighted move strongly changes relative weights.
The market transitions into a regime better suited to another smoother.
Leader changes can help reveal how the ensemble is adapting.
For example:
A shift toward HMA or DEMA may reflect stronger preference for responsive methods.
A shift toward SMA or RMA may reflect better recent performance from slower methods.
A shift toward LSMA may occur during a smooth local directional path.
These interpretations are contextual and should not be treated as fixed rules.
Gradient fill
The indicator fills the area between price and the ensemble line.
When price is above the line:
A bullish gradient is displayed.
When price is below the line:
A bearish gradient is displayed.
The gradient visually separates price from the adaptive trend estimate.
The fill reflects price location, while the line colour reflects the slope-derived ensemble trend.
These can temporarily disagree.
For example:
Price may fall below a still-rising ensemble during a pullback.
Price may rise above a still-falling ensemble during a counter-trend rally.
This disagreement can provide useful context.
Consensus glow
A glow is drawn around the ensemble line.
Its brightness changes according to weighted consensus.
When consensus is high:
The glow becomes brighter and more visible.
When the experts are divided:
The glow becomes more transparent.
The glow width is scaled using ATR based on the Base Length, helping the effect remain proportional across instruments and volatility environments.
The glow is a visual representation of model agreement. It does not modify the line or trend calculation.
Candle colouring
Candles can be coloured according to the current ensemble trend:
Bullish trend uses the selected bullish colour.
Bearish trend uses the selected bearish colour.
Candle colouring is based on the direction of the ensemble line, not the direction of each individual candle.
A bearish candle can therefore remain green during a bullish ensemble regime, and a bullish candle can remain red during a bearish regime.
How to interpret the indicator
Bullish ensemble trend
A bullish state means the final ensemble line is rising.
This indicates that the current weighted combination of experts is moving upward.
It does not require all individual experts to be bullish.
Bearish ensemble trend
A bearish state means the final ensemble line is falling.
The weighted combination is moving downward, even if one or more individual experts remain bullish.
High bullish consensus
A strongly positive vote means most influential expert weight is assigned to rising methods.
This can indicate broad directional alignment.
High bearish consensus
A strongly negative vote means the influential experts are predominantly falling.
Low consensus
A consensus near zero means weighted expert directions are divided.
This can occur during:
Trend transitions.
Sideways ranges.
Pullbacks.
Disagreement between faster and slower methods.
Low consensus does not automatically mean price will remain sideways. It means the ensemble's components are not currently aligned.
High leader weight and high consensus
This indicates that:
One method currently dominates.
The broader weighted bank is aligned with it.
The model is highly concentrated and directionally unified.
This can produce a responsive and decisive ensemble, but it also means the output depends heavily on the current leader.
Distributed weights and high consensus
This means several experts maintain meaningful weights while pointing in the same direction.
The trend is supported by a more diversified group of methods.
Leader weight high but consensus low
This can occur when the dominant expert points one way while several remaining experts point the other way.
The ensemble may still follow the leader, but internal disagreement is present.
How to use the indicator
1. Trend regime filter
Use the ensemble slope as directional context:
Prioritise long setups during bullish regimes.
Prioritise short setups during bearish regimes.
The indicator does not define entry price, stop placement or profit targets.
2. Consensus filter
A user may require stronger consensus before acting on the trend state.
For example:
A bullish flip with low consensus may represent an early or uncertain transition.
A bullish regime with high consensus indicates broader weighted alignment.
No universal consensus threshold is appropriate for every market.
3. Pullback analysis
During a bullish ensemble regime:
Price moving toward or below the line may represent a pullback.
The ensemble remaining bullish suggests its trend estimate has not yet reversed.
During a bearish regime:
Price moving toward or above the line may represent a counter-trend rally.
Price interaction with the line should be combined with structure and risk management.
4. Regime adaptation observation
The Leading Method label can be used to study how different smoothers perform through changing environments.
Rather than assuming one moving average is always best, the user can observe:
Which expert gains weight during trends.
Which expert takes over during transitions.
How concentrated the model becomes.
How quickly weights change under different Learning Rates.
5. Bullish and bearish flips
Trend flips can be used as:
Regime-change alerts.
Confirmation for another setup.
Potential exit conditions.
A directional filter for discretionary trades.
Because flips are based on line slope, responsive settings can generate repeated changes during ranges.
Suggested configurations
Balanced adaptive configuration
Moderate Base Length.
Moderate Learning Rate.
Directional loss.
Small positive Weight Floor.
Minimal Line Smoothing.
This keeps the model adaptive while preserving some expert diversity.
Fast adaptation configuration
Shorter Base Length.
Higher Learning Rate.
Magnitude-weighted loss.
Zero or very small Weight Floor.
Line Smoothing of 1 or 2.
This allows rapid concentration around recent winners but can create unstable leader changes.
Conservative diversified configuration
Longer Base Length.
Lower Learning Rate.
Directional loss.
Positive Weight Floor.
Additional Line Smoothing.
This creates slower and more diversified adaptation.
Large-move-focused configuration
Magnitude-weighted loss can be used when mistakes during large ATR-normalised moves should matter more than errors during minor fluctuations.
This may reduce the influence of small alternating bars on the weight distribution.
Pure directional configuration
Directional loss is useful when every close-to-close directional observation should be treated equally.
It creates a straightforward right-or-wrong scoring process.
How this differs from averaging moving averages
A normal moving-average ribbon or composite may calculate:
Average of SMA, EMA, HMA and other methods.
If every method receives equal weight permanently, its influence never changes.
Adaptive Trend Ensemble instead calculates:
Performance-dependent weights.
Sequential loss updates.
A dynamically changing weighted output.
Two bars with the same expert values can produce different ensemble values if the weight distributions differ.
How this differs from selecting the current fastest average
The indicator does not select whichever moving average is currently closest to price or whichever has moved the most.
Weights are based on whether previous expert slopes correctly anticipated realised price direction.
An expert can therefore lead even if it is not the fastest or closest line.
How this differs from an optimisation
The model does not search historical data for one set of parameters with the best backtest result.
It does not change the shared length of each expert.
Instead, it performs continuous online adaptation of the expert weights.
This avoids permanently selecting one historical winner, but it also means recent performance can strongly influence the current model.
How this differs from a machine-learning forecast
The indicator uses a genuine online-learning algorithm, but it is not a neural network or a price-target forecasting model.
It does not estimate the size of the next move.
The experts make binary directional predictions derived from their slopes.
The learning system then adjusts how much influence each moving-average value receives.
It is therefore best understood as an adaptive model-selection and blending process.
Causality and real-time behaviour
The learning update uses:
The prior-bar slope of each expert.
The current close-to-close realised direction.
It does not use future bars.
On historical completed candles, the update is fully causal.
On the current live candle:
The close can continue changing.
The realised direction can change.
Expert values can change.
Weights and consensus can update intrabar.
A bullish or bearish flip may appear before the candle closes.
Users requiring confirmed signals should evaluate the indicator at bar close.
Strengths
Combines eight distinct smoothing methods.
Adapts expert influence through online learning.
Supports directional and magnitude-sensitive losses.
Uses multiplicative updates rather than fixed weighting.
Provides optional protection against permanent weight collapse.
Separates ensemble direction from expert consensus.
Displays the currently leading method.
Uses one shared horizon for a fairer expert comparison.
Requires no offline training process.
Provides transparent open-source calculations.
Summary
Adaptive Trend Ensemble combines eight moving-average experts using a multiplicative online-learning model.
Each expert uses the same Base Length but applies a different smoothing method. The previous slope of each expert acts as its directional prediction for the latest close-to-close move.
After the realised direction is observed, incorrect experts receive either a fixed directional loss or an ATR-normalised magnitude-weighted loss. Their weights are reduced using an exponential Hedge update, then normalised and optionally adjusted using a minimum Weight Floor.
The current expert values are blended according to these adaptive weights, producing one ensemble line whose effective behaviour changes as different methods gain or lose influence.
A separate weighted vote measures current directional agreement. This consensus controls the visual glow and is displayed beside the current leading expert.
The result is a transparent adaptive trend model that does not assume one moving average will remain optimal. Instead, it continuously redistributes influence toward the methods that have recently aligned better with realised price direction while retaining configurable control over responsiveness, diversity and visual smoothing.
Indicador
Innovation-Gated Hull Supertrend [BackQuant] Innovation-Gated Hull Supertrend
Overview
Innovation-Gated Hull Supertrend is an adaptive trend-following overlay that combines three distinct signal-processing components:
A Hull Moving Average projection for responsive trend estimation.
An innovation-gated recursive filter for adaptive noise reduction.
A volatility-based Supertrend applied to the filtered Hull estimate.
The indicator is designed to behave differently during quiet and active market conditions.
When the Hull estimate changes only slightly relative to recent volatility, the innovation gate restricts how much of that movement is admitted into the filtered trend estimate. The Supertrend bands can also expand during these quieter conditions, reducing sensitivity to minor fluctuations.
When a larger and statistically more meaningful change occurs, the gate opens. The recursive filter becomes more responsive, the Supertrend bands return closer to their base width, and the model is allowed to react more quickly.
The result is a trend framework that attempts to balance two competing requirements:
Remain stable when price movement is small and noisy.
Respond more quickly when new information produces a meaningful displacement.
The indicator does not predict future prices. It is a causal trend model that adapts its response according to the size of newly arriving information relative to the current volatility environment.
Core calculation chain
The complete calculation can be summarised as:
Calculate a Hull Moving Average projection from the selected price source.
Estimate current volatility using ATR, standard deviation, or a blend of both.
Compare the Hull projection with the recursive filter’s previous estimate.
Normalise that difference by volatility to calculate an innovation score.
Pass the score through a smooth logistic gate.
Use the gate to adapt the recursive filter’s measurement and process uncertainty.
Generate the innovation-filtered Hull estimate.
Optionally adapt the Supertrend band multiplier using the same gate.
Apply Supertrend logic around the filtered Hull estimate.
Generate bullish and bearish regime changes when the Supertrend changes sides.
Each stage solves a different problem.
The Hull projection provides a responsive directional input. The innovation filter decides how much of that input should be trusted. The Supertrend then converts the filtered estimate into a persistent trailing regime.
Historical background
The indicator combines ideas from several areas of technical analysis and signal processing.
Hull Moving Average
The Hull Moving Average was developed by Alan Hull as a method of reducing lag while preserving a smooth output.
Traditional moving averages face a basic trade-off:
Short averages respond quickly but contain more noise.
Long averages are smoother but react later.
The Hull Moving Average attempts to improve this balance by combining weighted moving averages of different lengths.
Its general construction is:
Fast WMA = WMA of price over approximately half the main length.
Slow WMA = WMA of price over the full length.
Raw Hull = 2 × Fast WMA - Slow WMA.
Final Hull = WMA of the Raw Hull over the square root of the main length.
The subtraction stage compensates for some of the delay introduced by the longer average. The final square-root smoothing stage reduces noise in the compensated series.
Recursive estimation and the Kalman-filter principle
The innovation filter is based on the general recursive-estimation framework associated with Kalman filtering.
The Kalman filter was developed by Rudolf E. Kálmán and became widely used in engineering, navigation, aerospace, robotics and control systems.
A recursive estimator typically follows two stages:
Predict the current state from the previous state.
Correct that prediction using the newest observation.
The correction depends on how uncertain the model is and how reliable the new observation is believed to be.
The difference between the observation and prediction is called the:
Innovation
In this indicator:
The observation is the current Hull projection.
The prediction is the previous filtered estimate.
The innovation is the difference between them.
A large innovation means the Hull projection has moved significantly away from the model’s prior estimate.
A small innovation means the new observation is close to what the model already expected.
Supertrend
Supertrend is a volatility-trailing concept built from an underlying price reference and ATR-based bands.
Its basic structure consists of:
An upper band above the reference.
A lower band below the reference.
One-sided trailing behaviour.
A regime switch when price crosses the opposing band.
In a bullish regime, the lower band acts as the active trail.
In a bearish regime, the upper band acts as the active trail.
This indicator modifies the conventional approach in two important ways:
The central reference is the innovation-filtered Hull estimate rather than a normal price midpoint.
The band multiplier can adapt according to the innovation gate.
Stage 1: Hull projection
The first stage calculates the Hull projection from the selected price source.
The script determines:
The full Hull length.
A half-length rounded to a valid integer.
A square-root length rounded to a valid integer.
It then calculates:
Fast WMA = WMA(source, half length)
Slow WMA = WMA(source, full length)
Raw Hull = 2 × Fast WMA - Slow WMA
Hull Projection = WMA(Raw Hull, square-root length)
The Hull projection is more responsive than many conventional moving averages of a similar nominal length.
However, responsiveness also means it can react to short-lived movements. For that reason, the Hull projection is not used directly as the final trend line. It becomes the observation supplied to the innovation filter.
Hull Length
The Hull Length controls the underlying trend horizon.
Lower values:
React more quickly.
Follow shorter trend legs.
Produce more local changes.
Admit more short-term noise into the next stage.
Higher values:
Produce a smoother projection.
Focus on broader trend structure.
Respond later to sudden reversals.
The Hull Length therefore controls the basic timescale of the model before any adaptive filtering or Supertrend logic is applied.
Stage 2: Volatility model
The innovation must be interpreted relative to current market conditions.
A movement of 10 points may be large in a quiet market but insignificant in a highly volatile market.
The indicator therefore normalises the innovation using a selectable volatility estimate.
Three modes are available:
ATR
Standard Deviation
Blend
ATR mode
Average True Range measures recent trading range while accounting for gaps from the previous close.
True Range is based on the greatest of:
Current high minus current low.
Absolute current high minus previous close.
Absolute current low minus previous close.
ATR then smooths True Range across the selected Volatility Length.
ATR is useful because it measures the realised movement range of the instrument.
It is sensitive to:
Wide candles.
Price gaps.
Range expansion.
Standard Deviation mode
Standard deviation measures how widely the Hull projection has varied around its recent mean.
It is a dispersion measure rather than a range measure.
Standard deviation responds to:
Variation in the selected series.
Directional displacement.
Changes in the distribution of the filtered input.
While ATR focuses on bar range, standard deviation focuses on dispersion of the Hull series itself.
Blend mode
Blend mode calculates the average of ATR and standard deviation.
Conceptually:
Blended Volatility = (ATR + Standard Deviation) / 2
This provides a combined estimate incorporating:
Observed range behaviour.
Statistical dispersion of the Hull projection.
Neither measure is universally superior. The blend attempts to reduce dependence on only one definition of volatility.
Volatility Length
The Volatility Length controls how quickly the normalisation baseline changes.
Lower values:
React faster to recent volatility changes.
Cause the innovation score to adjust more quickly.
May make the gate less stable.
Higher values:
Produce a slower volatility baseline.
Create more consistent normalisation.
May respond later when volatility changes abruptly.
The volatility estimate is prevented from falling below the instrument’s minimum tick size, avoiding unstable division during extremely quiet periods.
Stage 3: Innovation calculation
The filter begins each bar with a prediction.
In this implementation, the prediction is the previous filtered estimate.
The innovation is:
Innovation = Hull Projection - Previous Filter Estimate
The innovation may be positive or negative.
A positive value means the Hull projection is above the prior estimate.
A negative value means it is below the prior estimate.
The absolute innovation measures the size of the disagreement regardless of direction.
Innovation score
The raw innovation is normalised by current volatility:
Innovation Score = |Innovation| / Volatility
This expresses the new movement in volatility units.
For example:
A score of 0.25 means the innovation is approximately one quarter of the selected volatility measure.
A score of 1.00 means it is approximately equal to that volatility measure.
A score above 1.00 means the change is larger than the current volatility baseline.
The score is dimensionless, making it more comparable across instruments and price scales.
This is the key quantity used to determine whether the filter should remain cautious or become more responsive.
Stage 4: Logistic innovation gate
The innovation score is passed through a logistic function.
The logistic function has the form:
Gate = 1 / (1 + exp(-x))
Its output remains between zero and one.
In the indicator, the gate input depends on:
Innovation Score
Innovation Threshold
Gate Sharpness
Conceptually:
Gate Input = Sharpness × (Score - Threshold)
When the score is below the threshold:
The gate approaches zero.
The filter treats the new Hull movement cautiously.
When the score rises above the threshold:
The gate moves toward one.
The filter becomes more willing to admit the new movement.
The logistic function creates a smooth transition rather than a hard on/off switch.
This is important because a binary threshold could cause abrupt changes whenever the score moves slightly above or below one exact value.
Innovation Threshold
The Innovation Threshold determines where the gate begins moving from a quiet state toward an active state.
Higher values:
Require a larger volatility-normalised innovation.
Keep the filter conservative for longer.
Reject more moderate changes.
Lower values:
Open the gate sooner.
Increase responsiveness.
Allow smaller movements to influence the estimate.
The threshold should be interpreted in relation to the selected volatility model.
Gate Sharpness
Gate Sharpness controls how rapidly the logistic gate transitions around the threshold.
Lower sharpness:
Creates a gradual transition.
Produces a wider intermediate region.
Changes responsiveness smoothly.
Higher sharpness:
Makes the gate behave more like a hard switch.
Creates a faster transition near the threshold.
Produces stronger separation between quiet and active states.
An extremely high value can make the adaptive behaviour abrupt, while a low value may reduce the distinction between quiet and active conditions.
Admission Floor
The gate is converted into an admission value.
The Admission Floor ensures that the filter never completely ignores the Hull projection.
The admission calculation is:
Admission = Floor + (1 - Floor) × Gate
When the gate is near zero:
Admission remains near the selected floor.
When the gate is near one:
Admission approaches one.
A lower floor creates stronger filtering during quiet conditions.
A higher floor keeps the model more responsive even when innovation is small.
This setting prevents the estimator from becoming fully frozen.
Stage 5: Adaptive recursive update
The admission and gate values modify two uncertainty terms:
Measurement noise.
Process noise.
These terms control how the recursive filter balances its existing estimate against the new Hull observation.
Measurement Noise
Measurement Noise represents uncertainty in the incoming Hull projection.
Higher measurement noise tells the filter:
Trust the new observation less.
Remain closer to the previous estimate.
Produce more smoothing.
Lower measurement noise tells the filter:
Trust the Hull projection more.
Correct the estimate more aggressively.
Become more responsive.
The script adapts measurement noise using the admission value:
Adaptive Measurement Noise = Base Measurement Noise / Admission
When admission is low:
Measurement noise increases.
The new Hull movement receives less weight.
When admission is high:
Measurement noise moves closer to its base value.
The filter becomes more receptive.
Process Noise
Process Noise represents uncertainty in the filter’s current state model.
Higher process noise tells the estimator:
The underlying trend may be changing.
The previous estimate may no longer be reliable.
Allow faster adaptation.
Lower process noise tells it:
Assume the existing state remains relatively stable.
Change the estimate more cautiously.
The script increases process noise as the gate opens:
Adaptive Process Noise = Base Process Noise × (1 + Process Boost × Gate)
This creates a two-sided adaptive response.
During quiet conditions:
Measurement noise increases.
Process noise remains closer to its base level.
The filter resists small changes.
During high-innovation conditions:
Measurement noise decreases toward its normal value.
Process noise increases.
The filter becomes substantially more responsive.
Process Boost
Process Boost controls how strongly the process uncertainty expands when the gate opens.
Higher values:
Allow faster response to large innovations.
Increase the filter gain during active movement.
Can make the model more sensitive after shocks.
Lower values:
Keep behaviour closer to the base recursive filter.
Produce more controlled adaptation.
May respond more slowly to genuine regime changes.
Covariance and filter gain
The recursive filter maintains an internal covariance representing uncertainty in its estimate.
Before the new observation is processed:
Predicted Covariance = Previous Covariance + Adaptive Process Noise
The filter gain is then:
Gain = Predicted Covariance / (Predicted Covariance + Adaptive Measurement Noise)
The gain remains between zero and one.
A low gain means:
The previous estimate receives more influence.
The Hull observation receives less influence.
A high gain means:
The filter moves more strongly toward the current Hull projection.
The new estimate is:
Filtered Hull = Prediction + Gain × Innovation
The covariance is then updated for the next bar.
Why the filter is innovation-gated
A normal recursive filter may use constant process and measurement noise settings.
That means its responsiveness is broadly fixed.
This indicator changes those terms according to the size of the innovation.
The model therefore behaves differently under two broad conditions.
Quiet condition
When the Hull projection remains close to the prior estimate relative to volatility:
Innovation score is low.
Gate remains mostly closed.
Admission is limited.
Adaptive measurement noise rises.
Process noise remains lower.
Filter gain falls.
The filtered Hull changes more slowly.
Active condition
When the Hull projection moves meaningfully away from the prior estimate:
Innovation score rises.
Gate opens.
Admission approaches one.
Measurement noise decreases.
Process noise increases.
Filter gain rises.
The estimate adapts more quickly.
This allows the model to filter small movement without applying the same degree of resistance to every large move.
Stage 6: Innovation-adaptive Supertrend bands
The filtered Hull becomes the centre of the Supertrend calculation.
The initial raw bands are:
Upper Band = Filtered Hull + Factor × ATR
Lower Band = Filtered Hull - Factor × ATR
The Supertrend uses its own ATR Period, which is independent of the volatility length used by the innovation score.
This distinction is important:
Innovation volatility determines whether the filter should admit new information.
Supertrend ATR determines the distance of the trailing regime bands.
Adaptive band factor
When Adapt Bands With Innovation is enabled, the Supertrend factor changes according to the gate.
The adaptive factor is:
Adaptive Factor = Base Factor ×
When the gate is near one:
The adaptive factor approaches the base factor.
Bands become relatively tighter.
The Supertrend can respond more readily.
When the gate is near zero:
The factor expands above its base value.
Bands become wider.
Minor price fluctuations are less likely to cause a reversal.
This creates coordinated adaptation:
Quiet conditions produce stronger filtering and wider bands.
Active conditions produce faster filtering and narrower bands.
The same innovation state therefore influences both the centre estimate and the trailing threshold.
Quiet Band Expansion
Quiet Band Expansion controls how much wider the Supertrend factor becomes when the innovation gate is closed.
A value of zero disables the expansion effect even if band adaptation is enabled.
Higher values:
Create wider bands during low-innovation conditions.
Reduce quiet-market reversals.
Delay new signals until price moves further.
Lower values:
Keep the adaptive factor closer to its base setting.
Allow more responsive regime changes.
The expansion is greatest when the gate is near zero and fades as the gate opens.
Supertrend trailing logic
The raw upper and lower bands are converted into one-sided trailing bands.
The lower band is prevented from moving downward while price remains above its previous value.
The upper band is prevented from moving upward while price remains below its previous value.
This ratcheting behaviour creates:
A rising lower trail during bullish conditions.
A falling upper trail during bearish conditions.
A trend change occurs when price crosses the active opposing boundary.
In a bullish regime:
The lower band is the active Supertrend.
In a bearish regime:
The upper band is the active Supertrend.
ATR Period and Factor
ATR Period
Controls the volatility horizon used to construct the Supertrend bands.
Lower values:
React faster to current range changes.
Produce more variable band widths.
Higher values:
Produce a steadier range estimate.
Respond more slowly to sudden volatility changes.
Factor
Controls the base distance between the filtered Hull and the Supertrend bands.
Lower factors:
Create tighter bands.
Produce earlier regime changes.
Increase sensitivity to noise.
Higher factors:
Create wider bands.
Produce fewer regime changes.
Increase confirmation delay.
When adaptation is enabled, the selected factor acts as the minimum or active-condition factor. Quiet conditions may expand it further.
Trend signals
The indicator generates a long signal when the Supertrend changes into its bullish state.
It generates a short signal when the Supertrend changes into its bearish state.
The signal requires the completed calculation chain:
Hull projection.
Innovation filtering.
Adaptive band factor.
Supertrend regime change.
The plotted symbols are:
𝕃 for a bullish transition.
𝕊 for a bearish transition.
These markers identify regime changes. They are not complete trading systems and do not define stop placement, position size or profit targets.
Innovation impulse alert
The script also includes an Innovation Impulse alert.
This occurs when the innovation score crosses above the selected Innovation Threshold.
It indicates that:
The difference between the Hull projection and the recursive estimate has become large relative to volatility.
The gate is entering a more active state.
The filter is beginning to admit new information more aggressively.
An innovation impulse does not necessarily produce an immediate Supertrend reversal.
It can occur:
During acceleration within an existing trend.
At the beginning of a possible regime change.
During a temporary volatility shock.
It is therefore best interpreted as an information-arrival event rather than an automatic long or short signal.
Visual components
Hull Projection
Displays the unfiltered Hull Moving Average input.
This is useful for comparing:
The responsive raw projection.
The innovation-filtered result.
The final Supertrend.
The Hull projection will generally react first.
Filtered Hull
Displays the recursive innovation-gated estimate.
The distance between the Hull projection and filtered Hull helps illustrate the filter’s current behaviour.
During quiet conditions:
The filtered Hull may lag behind small changes.
During meaningful innovations:
It can move more rapidly toward the Hull projection.
IGH Supertrend
Displays the final volatility trail around the filtered Hull.
It is the primary regime output.
The line is coloured according to the persistent bullish or bearish trend state.
Candle colouring
Candles may be coloured according to the active Supertrend regime:
Bullish colour during the long regime.
Bearish colour during the short regime.
This provides immediate chart-wide directional context.
How to interpret the indicator
Bullish regime
A bullish regime indicates that price has crossed into the bullish side of the adaptive Supertrend structure.
The active trail is positioned below the market and can be interpreted as:
A dynamic trend boundary.
A possible pullback reference.
A regime invalidation guide.
Bearish regime
A bearish regime indicates that price has crossed into the bearish side of the adaptive structure.
The active trail is positioned above the market and may act as:
Dynamic resistance.
A rally reference.
A bearish regime invalidation guide.
Low innovation score
A low score means the current Hull movement is small relative to volatility.
The model responds by:
Filtering more strongly.
Reducing admission.
Using a lower recursive gain.
Potentially expanding the Supertrend bands.
This is intended to reduce reactions to small fluctuations.
High innovation score
A high score means the Hull projection has changed substantially relative to volatility.
The model responds by:
Opening the gate.
Increasing admission.
Increasing process uncertainty.
Raising the filter gain.
Reducing quiet-condition band expansion.
This allows a faster response when the incoming information is more significant.
Rising Hull without a trend flip
The Hull projection may turn before the filtered Hull or Supertrend.
This means:
The fast input has changed.
The adaptive filter has not yet admitted enough of that change.
The Supertrend boundary has not yet been crossed.
This is not an error. It demonstrates the staged confirmation design.
Innovation impulse without trend reversal
An innovation impulse can occur without a long or short signal.
This may indicate:
Acceleration in the existing trend.
A volatility shock.
An attempted reversal that has not crossed the Supertrend.
The Supertrend remains the final regime layer.
How to use the indicator
1. Trend regime filter
Use the active Supertrend state to filter another entry method:
Prioritise long setups during bullish regimes.
Prioritise short setups during bearish regimes.
2. Pullback framework
In a bullish regime, pullbacks toward the Supertrend may represent tests of the active trend boundary.
In a bearish regime, rallies toward the Supertrend may represent resistance tests.
A touch alone does not guarantee continuation.
3. Innovation monitoring
The innovation alert can be used to identify when the model detects a meaningful change in its input.
This may help direct attention to:
Fresh acceleration.
Breakout attempts.
Possible trend transitions.
4. Confirmation framework
The three optional lines can be read as a progression:
Hull projection changes first.
Filtered Hull adapts according to innovation.
Supertrend confirms the final regime.
This allows users to study the difference between early movement and confirmed structure.
5. Trailing risk reference
The final Supertrend may be used as a visual trailing reference.
However, it does not account for:
Account size.
Position size.
Slippage.
Liquidity.
Maximum acceptable loss.
It should not replace a complete risk-management process.
Parameter interaction
The settings should not be tuned independently without considering how they interact.
More responsive configuration
A more responsive setup may use:
Lower Hull Length.
Lower Innovation Threshold.
Higher Admission Floor.
Lower Measurement Noise.
Higher Process Noise or Process Boost.
Lower Supertrend Factor.
Lower Quiet Band Expansion.
This will generally produce earlier changes but more noise.
More conservative configuration
A more conservative setup may use:
Higher Hull Length.
Higher Innovation Threshold.
Lower Admission Floor.
Higher Measurement Noise.
Lower Process Boost.
Higher Supertrend Factor.
Higher Quiet Band Expansion.
This will generally create fewer transitions but greater delay.
Balanced interpretation
Changing several settings in the same direction can produce an extreme result.
For example:
A very low threshold, high admission floor, large process boost and tight Supertrend factor may overreact.
A very high threshold, low admission floor, high measurement noise and wide Supertrend factor may respond excessively slowly.
The appropriate balance depends on the instrument, timeframe and intended holding period.
How this differs from a standard Hull trend indicator
A standard Hull trend indicator normally uses:
Hull slope.
Price crossing the Hull.
A fast and slow Hull comparison.
This indicator instead:
Uses the Hull as an observation.
Measures its disagreement with a recursive estimate.
Normalises that disagreement by volatility.
Adapts the filter gain according to the innovation.
Applies a final Supertrend regime around the filtered result.
The Hull is therefore the beginning of the model, not the final signal.
How this differs from a fixed Kalman-style filter
A fixed recursive filter uses constant uncertainty settings.
Innovation-Gated Hull Supertrend adapts both measurement and process uncertainty according to the normalised innovation.
This means:
Small innovations are filtered more heavily.
Large innovations receive greater admission.
The response speed is therefore state dependent.
How this differs from a standard Supertrend
A standard Supertrend is commonly centred around a raw price reference such as HL2.
This indicator uses:
A responsive Hull projection.
An innovation-gated recursive estimate of that projection.
An optionally adaptive band multiplier.
The Supertrend is therefore built around a filtered trend estimate rather than raw price alone.
Strengths
Combines responsive and stable trend-processing stages.
Normalises new movement by current volatility.
Uses a smooth gate rather than a binary threshold.
Adapts measurement and process uncertainty.
Can widen trend bands during quiet conditions.
Can respond more rapidly to meaningful innovations.
Separates early movement from final regime confirmation.
Supports ATR, standard deviation and blended volatility models.
Provides trend, impulse and visual comparison outputs.
Limitations
The indicator is reactive rather than predictive.
Strong filtering can delay genuine reversals.
Responsive settings can increase whipsaws.
A large innovation may represent a temporary shock rather than a lasting trend.
Supertrend signals still depend on ATR and price crossing behaviour.
Parameter combinations can materially change the model’s behaviour.
The indicator may require different settings across assets and timeframes.
The recursive state develops from the available chart history.
Values can update while the current real-time candle is still forming.
Causality and real-time behaviour
The calculation uses current and historical observations without future-looking references.
However, like most indicators calculated on live candles, the current bar’s values can change before the candle closes.
This means:
The Hull projection may move intrabar.
The innovation score and gate may change intrabar.
A Supertrend transition may appear and disappear before confirmation.
Users requiring confirmed signals should evaluate the indicator at bar close or configure alerts accordingly.
Alerts
The indicator provides three alert conditions:
IGH ST Long: the adaptive Supertrend changes into a bullish regime.
IGH ST Short: the adaptive Supertrend changes into a bearish regime.
IGH Impulse: the normalised innovation score crosses above the selected threshold.
The impulse alert identifies increased information flow into the filter. It does not specify direction by itself because the innovation score uses the absolute size of the prediction error.
Summary
Innovation-Gated Hull Supertrend combines a responsive Hull Moving Average, a volatility-normalised innovation gate, an adaptive recursive filter and a volatility-trailing Supertrend.
The Hull projection provides an early estimate of directional movement. The recursive filter compares that projection with its prior state and measures the resulting innovation relative to ATR, standard deviation or a blend of both.
A logistic gate then determines how strongly the new movement should be admitted. During quiet conditions, the filter becomes more conservative and the Supertrend bands can expand. During meaningful displacement, the filter becomes more responsive and the bands move closer to their base width.
The final Supertrend converts the adaptive estimate into a persistent bullish or bearish regime.
The indicator is designed to make responsiveness conditional rather than fixed: small movements receive stronger filtering, while larger volatility-adjusted innovations are allowed to influence the model more quickly.
Indicador
VWAP Deviation Trend [BackQuant]VWAP Deviation Trend
Overview
VWAP Deviation Trend is a volume-weighted trend-following overlay that transforms VWAP and its surrounding price distribution into a directional trailing structure.
Rather than using VWAP only as a fair-value line, the indicator calculates:
A configurable anchored or rolling VWAP.
The volume-weighted standard deviation of price around that VWAP.
Adaptive upper and lower deviation bands.
One-sided trailing boundaries used to confirm bullish and bearish regimes.
The indicator is designed to identify when price has moved far enough away from accepted volume-weighted value to establish a meaningful directional shift.
Unlike a simple VWAP crossover, price can move through VWAP without immediately changing the active trend. A new regime requires price to break the opposite trailing deviation boundary, optionally with confirmation from the direction of VWAP itself.
The updated visual engine also measures trend strength and uses it to control:
Gradient intensity.
Trail glow width.
Post-flip bloom effects.
The visual separation between price and the active trail.
Core concept
VWAP represents the average price paid over a selected period, weighted by trading volume.
The basic formula is:
VWAP = Sum of Price × Volume / Sum of Volume
Prices associated with greater volume contribute more heavily to the final value. This makes VWAP a useful approximation of:
Volume-weighted fair value.
The center of traded activity.
The average position of market participants.
An institutional execution benchmark.
However, VWAP alone does not explain how widely price has been distributed around that value.
VWAP Deviation Trend treats VWAP as the center of a volume-weighted price distribution and measures the dispersion around it. That dispersion is then used to create trailing trend boundaries.
VWAP calculation modes
The indicator supports five VWAP windows:
4 Hours
Daily
Weekly
Rolling Lookback Bars
Rolling Lookback Days
4 Hours
Resets VWAP at fixed four-hour intervals.
This can be useful for:
Cryptocurrency markets.
Intraday futures.
Continuously traded markets.
Shorter fair-value regimes.
Daily
Resets at the beginning of each calendar day.
This is the traditional intraday VWAP structure and is useful for:
Session bias.
Intraday mean reversion.
Day-trading trend confirmation.
Weekly
Accumulates volume and price across the current week.
This creates a slower structural anchor suited to:
Swing trading.
Weekly positioning.
Broader accepted-value analysis.
Rolling Lookback Bars
Calculates VWAP over a fixed number of candles.
The window moves forward continuously and does not reset at a calendar boundary.
This is useful for:
Systematic trend models.
Consistent multi-timeframe analysis.
Markets where daily sessions are less important.
Rolling Lookback Days
Includes bars that fall within a selected number of calendar days.
This keeps the analytical window tied to elapsed time instead of a fixed candle count.
Anchored versus rolling VWAP
Anchored modes begin at a fixed boundary and accumulate until the next reset.
Rolling modes continually remove old observations as new observations arrive.
Anchored VWAP is useful when a particular session or week has structural meaning. Rolling VWAP is useful when the trader wants a stable and continuously adapting lookback.
Volume-weighted deviation
The indicator calculates more than the VWAP mean.
It also measures volume-weighted price variance using:
Weighted Mean Square = Sum of Price² × Volume / Sum of Volume
Weighted Variance = Weighted Mean Square - VWAP²
Weighted Deviation = Square Root of Weighted Variance
This measures how widely prices associated with meaningful trading volume are distributed around VWAP.
A small deviation suggests:
Trading is concentrated near fair value.
The market is relatively balanced.
Price acceptance is narrow.
A large deviation suggests:
Trading is spread across a wider range.
Price discovery is more active.
The market is less tightly centered around VWAP.
Because the calculation is volume weighted, high-volume prices influence the bands more than low-volume excursions.
Fallback when volume is unavailable
If usable volume is not available, the indicator falls back to an unweighted arithmetic mean and variance.
This allows it to function on synthetic or limited-volume symbols, although the result should then be interpreted as a rolling or anchored mean rather than a true VWAP.
Deviation bands
The raw width is calculated as:
Deviation Width = Weighted Deviation × Deviation Multiplier
The upper and lower raw bands are:
Upper Band = VWAP + Band Width
Lower Band = VWAP - Band Width
Higher deviation multipliers create wider bands and fewer trend changes.
Lower multipliers create tighter bands and faster, more frequent flips.
ATR minimum width
During low-dispersion periods, volume-weighted deviation can become extremely narrow.
This can cause small and insignificant movements to trigger repeated reversals.
The optional ATR floor calculates:
ATR Floor = ATR × ATR Minimum Multiplier
The final width becomes:
Band Width = Maximum of Deviation Width and ATR Floor
This preserves volume-weighted deviation as the primary band engine while preventing the channel from collapsing below a practical volatility threshold.
Trailing-band construction
The raw deviation bands move freely with VWAP and dispersion.
The indicator converts them into one-sided trailing levels.
Lower trail
While the selected trigger remains above the lower trail:
The trail can rise.
It cannot move downward.
This creates a ratcheting support structure.
Upper trail
While the trigger remains below the upper trail:
The trail can fall.
It cannot move upward.
This creates a ratcheting resistance structure.
The active trend trail is:
The lower trail during bullish regimes.
The upper trail during bearish regimes.
Why trailing logic matters
A raw VWAP band can move toward price and create unstable signals.
The one-sided trail preserves trend structure and creates hysteresis.
Hysteresis means the threshold required to enter a bullish regime is different from the threshold required to enter a bearish regime.
This allows price to rotate around VWAP without constantly changing the active trend.
Trend initialization
When the first valid VWAP is available:
The trend initializes bullish if the trigger is at or above VWAP.
The trend initializes bearish if the trigger is below VWAP.
After initialization, a full break of the opposite trail is required to change regimes.
Bullish trend flip
A bullish flip requires:
The selected trigger to move above the upper trailing band.
The current trend not already to be bullish.
VWAP slope confirmation to pass if enabled.
Once confirmed:
The trend becomes bullish.
The active trail moves beneath the market.
A bullish signal marker is displayed.
Bearish trend flip
A bearish flip requires:
The selected trigger to move below the lower trailing band.
The current trend not already to be bearish.
VWAP slope confirmation to pass if enabled.
Once confirmed:
The trend becomes bearish.
The active trail moves above the market.
A bearish signal marker is displayed.
Flip trigger
The trend can be triggered using:
Close
The selected VWAP price source
Close is the more conventional option.
Using the price source, such as HLC3, can produce a slightly smoother trigger because it reflects more of the bar than the close alone.
VWAP slope confirmation
Optional slope confirmation requires VWAP itself to move in the direction of the proposed new trend.
For a bullish flip:
Current VWAP must be above VWAP from the selected lookback.
For a bearish flip:
Current VWAP must be below its prior value.
This can help reject:
Temporary band breaks.
Low-volume price spikes.
Liquidity sweeps against flat fair value.
The tradeoff is additional confirmation delay.
Breaking the trail on flips
The active trail changes from one side of the market to the other during a regime transition.
The Break Trail On Flips option inserts a visual gap on the flip bar so the previous and new trails are not connected by a misleading line segment.
This affects presentation only.
Visual trend-strength engine
The updated script includes a visual-strength model that controls the intensity of the gradient and glow.
It combines two measurements:
Distance between price and the active trail.
Slope of VWAP relative to the current band width.
Distance strength
The script measures:
Absolute Distance = |Close - Trend Trail|
This is normalized by the current band width.
A larger distance indicates stronger separation between price and the structural trail.
Slope strength
VWAP movement across the slope lookback is also normalized by the band width.
This measures whether volume-weighted fair value itself is moving meaningfully relative to the size of the current deviation structure.
Combined trend strength
The final visual strength is weighted:
70% price-to-trail distance.
30% VWAP slope strength.
This produces a value between zero and one.
It does not change trend logic or signals. It controls the visual intensity of the indicator.
Layered gradient fill
Instead of using one flat gradient, the updated indicator divides the space between the trail and price into six visual layers.
The levels are placed progressively between:
The active trend trail.
The current closing price.
The gradient is:
Most concentrated near the structural trail.
Progressively softer toward price.
The opacity adapts to trend strength.
When price is strongly separated from the trail and VWAP is moving with the regime:
The gradient becomes more vivid.
When the trend is weak:
The fill becomes softer and more transparent.
This makes the visual ribbon encode more than direction. It also reflects the current strength of the price-to-structure relationship.
Flip bloom
After a confirmed trend flip, the indicator creates a temporary bloom around the new trail.
The bloom is strongest immediately after the transition and fades over the following bars.
Its intensity follows this general sequence:
First bar after flip: strongest bloom.
Second bar: reduced bloom.
Third bar: light residual bloom.
Afterward: bloom disappears.
This visually emphasizes fresh regime changes without permanently increasing chart brightness.
The bloom is cosmetic and does not affect calculation.
Adaptive trail glow
The glow surrounding the trail also changes with trend strength.
The base width is ATR-scaled, then increases slightly as the visual trend-strength score rises.
This creates:
A broader glow during stronger regimes.
A narrower glow when trend structure is weaker.
The glow contains:
An inner, more visible layer.
A wider, softer outer layer.
Visual interpretation
The updated presentation provides several pieces of information simultaneously:
Color shows the active trend direction.
The trail shows the structural regime boundary.
Gradient intensity reflects trend strength.
Glow width reinforces structural conviction.
The bloom highlights fresh regime transitions.
How to use the indicator
Trend regime filter
Use the active color and trail position as directional context:
Favor longs during bullish regimes.
Favor shorts during bearish regimes.
Pullback structure
In a bullish regime:
VWAP represents volume-weighted fair value.
The lower trail represents deeper structural support.
In a bearish regime:
VWAP represents the mean-reversion anchor.
The upper trail represents deeper structural resistance.
Trend-strength context
A vivid gradient and broader glow suggest:
Price is well separated from the trail.
VWAP is moving in the trend direction.
The regime has stronger structural momentum.
A weak or faded gradient suggests:
Price is closer to the trail.
VWAP slope is weaker.
The trend may be consolidating or losing strength.
Fresh transitions
The bloom helps identify newly established regimes.
A fresh flip with:
Strong bloom.
Growing price separation.
VWAP slope alignment.
generally represents stronger early trend structure than a flip that immediately loses visual intensity.
Dynamic risk management
The active trail may be used as:
A trailing stop reference.
A regime invalidation boundary.
A position-management guide.
Because the trail responds to both volume-weighted dispersion and volatility, it adjusts as market conditions change.
How this differs from a standard VWAP
A standard VWAP:
Plots only volume-weighted mean price.
Usually resets once per session.
Does not maintain trend state.
VWAP Deviation Trend:
Supports anchored and rolling windows.
Calculates volume-weighted dispersion.
Creates adaptive raw bands.
Converts them into directional trailing boundaries.
Maintains persistent bullish and bearish regimes.
Adds a strength-reactive visual system.
How this differs from Supertrend
A traditional Supertrend normally uses a central price such as HL2 and ATR-based bands.
VWAP Deviation Trend uses:
Volume-weighted fair value as the center.
Volume-weighted standard deviation as the primary width.
ATR only as an optional minimum floor.
This means the trail responds not only to range volatility, but also to where trading volume has been concentrated.
How this differs from Bollinger Bands
Bollinger Bands normally use:
A moving average.
Unweighted standard deviation.
Symmetrical non-trailing bands.
This indicator uses:
A volume-weighted mean.
Volume-weighted variance.
One-sided trailing bands.
Persistent trend-state logic.
It is therefore a trend-regime model rather than a standard mean-reversion envelope.
Input guide
VWAP Mode
Selects the anchored or rolling calculation window.
Deviation Multiplier
Controls the width of the statistical bands.
Higher values produce wider, slower regimes. Lower values produce tighter and faster regimes.
ATR Minimum Width
Prevents excessive narrowing during compressed conditions.
VWAP Slope Confirmation
Requires volume-weighted fair value to move with the proposed trend.
Flip Trigger
Selects whether close or the chosen price source must cross the trail.
Visual settings
Allow the trader to display:
The trend trail.
VWAP.
Raw deviation bands.
Layered gradient.
Adaptive glow.
Signals.
Trend candles.
Strengths
Combines fair value, dispersion, and trend structure.
Uses volume-weighted mean and variance.
Supports multiple anchored and rolling VWAP windows.
Uses ATR protection against narrow-band whipsaws.
Creates persistent regimes with hysteresis.
Provides optional VWAP slope confirmation.
Includes a trend-strength-reactive visual system.
Clearly emphasizes fresh trend transitions.
Limitations
Volume quality varies between instruments.
Anchored VWAP modes may be unstable immediately after a reset.
Long windows can react slowly to sudden regime changes.
Tight settings can increase whipsaws.
Wide settings can delay reversals.
Slope confirmation can add additional lag.
Visual strength is contextual and is not a separate trading signal.
Alerts
The indicator includes alerts for:
Confirmed bullish trend flips.
Confirmed bearish trend flips.
These represent complete VWAP deviation regime changes, not ordinary crosses of VWAP.
Summary
VWAP Deviation Trend converts volume-weighted fair value and price dispersion into a directional trend trail.
It calculates VWAP over a configurable anchored or rolling window, measures volume-weighted standard deviation around that VWAP, and builds upper and lower deviation bands. An optional ATR floor prevents the structure from becoming excessively narrow during quiet conditions.
The raw bands are transformed into one-sided trails. The lower trail ratchets upward during bullish regimes, while the upper trail ratchets downward during bearish regimes. Trend changes occur only when price breaks the opposite trail, optionally with confirmation from the slope of VWAP.
The updated visual engine measures price separation and VWAP slope to dynamically control the layered gradient, trail glow, and temporary post-flip bloom. This creates a clearer representation of direction, structural strength, and fresh regime transitions without changing the underlying signal logic. Indicador
Watermark Pro @SafarTradesWatermark Pro
Watermark Pro is a customizable branding and metadata overlay for TradingView charts. It helps create a clean, professional workspace while keeping important chart information consistently visible.
The indicator combines customizable branding, chart metadata, and account status badges into a single configurable layout, making it suitable for personal trading, screenshots, educational content, and social media publishing.
Branding Panel
Display a fully customizable title and subtitle with flexible positioning to maintain a consistent visual identity across all charts.
Account Status Badge
Display a customizable status badge (e.g., Live Account, Demo Account, Funded Account, Backtesting) with multiple styling options to clearly identify the chart environment.
Chart Metadata
Optionally display the current date, trading symbol, and timeframe in a dedicated information panel that updates automatically as charts change.
Customization
Every component can be customized independently, allowing you to configure the layout to match your personal workflow and visual preferences.
Theme presets
Branding panel
Account status badge
Chart metadata panel
Flexible positioning
Color and typography controls
Badge styling options
Intended Use
Watermark Pro is suitable for traders, educators, analysts, and content creators who want consistent chart branding and a clean presentation for trading, analysis, screenshots, and educational content. Indicador
ICT Sessions & Killzones - Asia London NY + Liquidity[LunqFX]ICT Sessions & Killzones is a modern smart-money session indicator for TradingView that maps the three global trading sessions — Asia, London and New York — as clean, colour-coded ranges and, unlike most session tools, automatically detects liquidity sweeps: the exact moment price raids a previous session's high or low and rejects it. It turns the daily rhythm of the market — the ICT killzones, session opens, and the liquidity pools left behind — into a clear, actionable map. Works on forex, crypto, indices, futures and gold (XAUUSD), on any intraday timeframe. Built in Pine Script v6. Keywords: ICT, killzones, sessions, Asia session, London session, New York session, liquidity, liquidity sweep, stop hunt, smart money concepts, SMC, session high low, opening range, forex, crypto, day trading, scalping.
◆ WHY SESSIONS MATTER
Price does not move randomly — it moves in sessions. Asia sets the range, London expands it, New York reverses or continues it. The highs and lows each session leaves behind become liquidity pools — resting stop orders that smart money targets. Knowing where those levels are, which session is active, and when a level gets swept is the core of session-based and ICT trading. This tool puts all of that on your chart automatically.
◆ WHAT IT DRAWS
Session boxes — Asia (violet), London (teal) and New York (gold) ranges drawn automatically from each session's high and low, kept across history so you can study the pattern.
Previous-session liquidity levels — the last completed session's high and low extended forward as dashed lines. These are the magnets price hunts next.
Liquidity sweep markers — a compact, colour-coded arrow (▲/▼ with the session code A / L / NY) printed when price wicks beyond a prior session extreme and closes back inside — a real stop-raid / rejection. Hover any marker for the full detail.
Neon gradient candles — turquoise up / magenta down, intensity scaled by momentum.
◆ THE LIVE DASHBOARD
A clean, colour-railed panel that reads the sessions at a glance:
Active session — which session is open right now (● marks any that are live; London and New York overlap in real hours, so both can be active).
Range per session — each session's high–low.
Range in pips — how far each session actually moved.
★ Widest range — the session that dominated the day (the "power session").
Timezone readout, fully themeable, adjustable text size.
◆ HOW IT WORKS
Every bar is assigned to a session from its own timestamp (no repainting from higher-timeframe data). The session's running high and low build the box in real time. When a new session opens, the previous session's extremes are locked in as liquidity levels. A liquidity sweep is flagged only when price trades beyond a prior session's high/low and then closes back inside it — a genuine rejection — so a clean break straight through does not trigger a false signal. This keeps the chart clean and every sweep meaningful.
◆ HOW TO USE IT
Trade the killzones. The London and New York opens produce the biggest, cleanest moves — focus your entries there.
Use prior session highs/lows as targets. Untapped levels act as magnets; price often runs them before reversing.
Fade or follow sweeps. When a sweep prints, the raid has taken liquidity — fade it back into range, or trade the reversal in the opposite direction.
Read the dashboard for context. Know which session is active and which had the widest range before you commit.
Set your times/timezone. Adjust each session's hours and the timezone in the settings to match your market and broker.
Combine with your own market structure, order blocks or bias for higher-probability confluence.
◆ SETTINGS
Session times & colours (Asia / London / New York), timezone, session boxes (soft fill or outline), previous-session levels with adjustable extension, liquidity sweep markers, neon candles, and a dashboard (show/hide, position, text size, background).
◆ ALERTS
Liquidity sweep — fires when any previous-session high or low is swept.
◆ LIMITATIONS
Sessions are an intraday concept — use a 1m to 4h timeframe. On daily or higher the panel shows a reminder and no sessions are drawn.
Default session times are in GMT; set the timezone and hours to match your instrument and broker feed, as session boundaries vary by symbol.
A liquidity sweep shows that a level was raided and rejected — it is context and confluence, not a standalone buy/sell signal.
Session ranges reflect the data of your chart's feed; different brokers can differ slightly.
◆ ORIGINALITY & NON-REPAINTING
Original work — the session engine, the rejection-based liquidity-sweep detection, the previous-session liquidity levels and the dashboard are all my own implementation; no third-party code is used. Sessions and levels are built from each bar's own timestamp with no higher-timeframe lookahead, so a sweep printed on a closed bar stays.
Educational analysis tool, not financial advice. Trading involves risk. Always do your own research and manage risk. © LunqFX. Indicador
NLMS Volatility Trail [BackQuant]NLMS Volatility Trail
Overview
NLMS Volatility Trail is an adaptive trend-following overlay that combines a machine-learning style adaptive filter with a volatility-based trailing structure. It is built around the Normalized Least Mean Squares (NLMS) algorithm, then converts that adaptive estimate into an ATR-based trailing line designed to follow directional regimes while filtering out minor noise.
The indicator has two core layers:
An NLMS adaptive filter , which learns a dynamic price estimate from prior bars.
An ATR volatility trail , which converts that learned estimate into a step-like directional trailing structure.
The goal is to produce a trend line that is more adaptive than a traditional moving average and more structured than a raw adaptive filter. The NLMS engine learns the underlying price path, while the ATR trail adds volatility-aware confirmation so trend shifts only occur when the adaptive estimate moves meaningfully.
Core idea
Most trend filters use fixed smoothing rules. An EMA, SMA, WMA, or HMA always applies the same mathematical weighting scheme regardless of whether the market is trending, ranging, expanding, or compressing.
NLMS is different. It continuously updates its internal weights based on prediction error.
This means the filter is not just averaging price. It is constantly asking:
How well did the previous weighting structure predict the current bar?
How large was the error?
How should the weights adjust to reduce future error?
The second layer then takes that adaptive estimate and applies an ATR-based trailing mechanism around it. This creates a volatility-adjusted trend trail that reacts to confirmed shifts while ignoring smaller movements that do not exceed the range structure.
What NLMS is
NLMS stands for Normalized Least Mean Squares . It is an adaptive filtering algorithm from digital signal processing. It is closely related to the original LMS algorithm developed by Bernard Widrow and Ted Hoff, which became one of the foundational online learning methods used in adaptive systems.
Adaptive filters have historically been used in:
Noise cancellation
Echo cancellation
Telecommunications
Radar and sonar processing
Signal prediction
Control systems
The basic purpose is to estimate or predict a signal while continuously adapting to changing conditions.
In trading terms, this indicator uses NLMS to build a learned estimate of price from prior bars.
How the NLMS filter works
The filter uses a set of historical inputs called taps .
If taps = 72, the model uses the previous 72 bars:
source
source
source
...
source
Each tap has a learned weight.
The prediction is calculated as:
prediction = w1 × source + w2 × source + ... + wM × source
The filter then compares the prediction to the actual current source:
error = source - prediction
That error drives the weight update.
If the prediction was poor, the weights adjust more.
If the prediction was accurate, the weights adjust less.
This creates an adaptive estimate that evolves with market behavior.
Why it is normalized
The normal LMS algorithm updates weights based on the raw input and prediction error. The issue is that if the input signal becomes large or volatile, updates can become unstable.
NLMS solves this by dividing the update by the input power:
power = sum(source ²)
The update becomes:
w = w + (μ / (ε + power)) × error × input
This normalization makes the learning process more stable across different volatility environments.
When the input power is high:
Updates are scaled down.
The filter avoids overreacting.
When the input power is low:
Updates are allowed to remain meaningful.
This is why NLMS is better suited to markets than a basic adaptive filter. Markets constantly shift between quiet and volatile regimes.
Weight initialization
The script initializes all weights equally:
weight = 1 / M
This means the filter starts with an SMA-like prior. Before learning begins, every historical bar contributes equally.
Over time, the filter adapts away from that equal-weight baseline and learns its own weighting structure.
Inputs that control the NLMS engine
Filter Taps (M)
Controls how many historical bars the model learns from.
Higher taps:
More memory
Smoother adaptive estimate
Slower response to regime change
Lower taps:
Less memory
Faster reaction
More noise sensitivity
Step Size (μ)
Controls the learning rate.
Lower μ:
Slower learning
Smoother output
More stable
Higher μ:
Faster learning
More responsive
Can become noisy if too aggressive
This is one of the most important settings. It controls how quickly the model changes its internal weights.
Regularization (ε)
Prevents instability when input power is very low.
It acts as a stabilizer in the denominator:
ε + power
Higher values make updates more conservative.
Lower values allow stronger adaptation but can become less stable in quiet conditions.
From adaptive filter to volatility trail
The raw NLMS output is not plotted directly as the main trend line. Instead, it is passed into a volatility trailing structure.
The script builds an ATR band around the NLMS estimate:
Upper band = NLMS output + ATR × factor
Lower band = NLMS output - ATR × factor
Then it creates a trailing value that only updates when the NLMS band structure forces it to move.
This creates a trail that behaves similarly to a volatility stop, but the center is not price or hl2. It is the learned NLMS estimate .
ATR volatility trail logic
The trail starts from the NLMS output, then carries forward its previous value:
nlmsAtr := previous nlmsAtr
Then:
If lower band rises above the trail, the trail moves up.
If upper band falls below the trail, the trail moves down.
This creates a directional trailing structure:
In bullish regimes, the trail ratchets upward.
In bearish regimes, the trail ratchets downward.
It filters out small movements because price must move enough relative to ATR and the adaptive estimate to change the trail direction.
Why combine NLMS with ATR
NLMS alone gives an adaptive estimate, but it can still wiggle as the model learns.
ATR alone gives volatility structure, but it is usually tied to raw price and fixed smoothing.
Combining them gives:
Adaptive intelligence from NLMS.
Volatility confirmation from ATR.
Cleaner trend state transitions.
Less dependence on fixed moving-average assumptions.
The NLMS model learns the underlying price behavior, while ATR decides whether movement is large enough to matter.
Trend direction
Trend flips are detected from the trail itself:
Bullish when nlmsAtr crosses above its previous value.
Bearish when nlmsAtr crosses below its previous value.
This means signals are generated when the volatility trail changes direction, not when price simply crosses the line.
That is important because:
The trail must structurally move.
The signal is tied to confirmed trail direction.
Noise around the line does not automatically create a flip.
Visual design
The indicator includes several visual layers.
Main trail line
The central plotted line is the NLMS ATR trail. It changes color based on the current trend state:
Green for bullish trail direction.
Red for bearish trail direction.
Gray before a trend state is established.
Gradient fill
The script fills the space between price and the trail:
If price is above the trail, bullish fill is shown.
If price is below the trail, bearish fill is shown.
The fill is stronger near the trail and fades toward price, making the trail feel like the active structural reference.
Trail glow
A soft glow is drawn around the trail using a small ATR offset:
glow = ATR(14) × 0.06
This highlights the trail visually without cluttering the chart.
Trend candles
Candles are colored by trend state:
Bullish trend = bullish candles.
Bearish trend = bearish candles.
This allows the script to function as a complete regime overlay.
How to interpret the indicator
Bullish state
A bullish state occurs when the NLMS volatility trail turns upward.
This suggests:
The adaptive filter is shifting higher.
The ATR trail has confirmed upward structure.
Trend pressure has turned bullish.
Bearish state
A bearish state occurs when the NLMS volatility trail turns downward.
This suggests:
The adaptive estimate is shifting lower.
The volatility trail has confirmed downside structure.
Trend pressure has turned bearish.
Price above the trail
Generally indicates bullish structure.
Price below the trail
Generally indicates bearish structure.
But the most important signal is the direction of the trail itself, not every price touch.
How to use it in practice
1) Trend following
Use the trail direction as the primary bias:
Favor longs when the trail is bullish.
Favor shorts when the trail is bearish.
2) Dynamic support/resistance
The trail can act like a dynamic structural level:
In uptrends, pullbacks toward the trail can act as support.
In downtrends, rallies toward the trail can act as resistance.
3) Trade management
The trail can be used as:
A trailing stop guide.
A regime invalidation level.
A trend continuation reference.
4) Regime filtering
Because the line adapts using NLMS and only flips when the volatility trail turns, it can be used to filter other entries:
Take only long setups during bullish trail regimes.
Take only short setups during bearish trail regimes.
Avoid countertrend trades when the trail is strongly directional.
Difference from normal Supertrend or ATR trails
A normal ATR trail is usually built directly from price or hl2.
This indicator is different because the trail is built around an adaptive learned estimate.
That means:
The centerline is not raw price.
It is not a fixed moving average.
It is a continuously learned NLMS estimate.
So the trail has a different character:
More adaptive than a standard moving average trail.
More stable than a raw price-based ATR stop.
More responsive to changing market structure than fixed filters.
Difference from the NLMS Adaptive Trend Filter
The NLMS Adaptive Trend Filter plots the learned estimate directly and reads trend from its slope.
NLMS Volatility Trail goes one step further:
It uses the learned estimate as the base.
Then wraps it with ATR structure.
Then turns that into a trailing regime line.
So this version is more structure-oriented and better suited for trailing trend behavior.
Parameter tuning
Taps
Use higher taps for smoother trend structure.
Use lower taps for faster adaptation.
Step Size
Use lower step size for stability.
Use higher step size for responsiveness.
Regularization
Use higher regularization when the filter feels unstable.
Use lower regularization when the filter is too sluggish.
ATR Period
Controls volatility estimate:
Shorter = more reactive trail.
Longer = smoother trail.
ATR Factor
Controls band width:
Higher factor = wider trail, fewer flips.
Lower factor = tighter trail, more flips.
Strengths
Combines adaptive filtering with volatility trailing logic.
Learns from market structure instead of using fixed weights.
Uses ATR to reduce noise and confirm meaningful movement.
Good for trend following and trailing stop frameworks.
Visually clean with gradient fill and candle coloring.
Limitations
Still reactive, not predictive.
Can lag during violent reversals.
High learning rates may create noise.
Low ATR factors may cause whipsaws.
Requires tuning for timeframe and asset volatility.
Summary
NLMS Volatility Trail combines an adaptive NLMS predictor with an ATR-based trailing structure. The NLMS layer continuously learns a dynamic estimate of price from historical bars, while the ATR trail converts that estimate into a cleaner directional regime line. This makes the indicator more adaptive than a traditional moving average and more structured than a raw adaptive filter. It is best used as a trend-following overlay, dynamic support/resistance guide, and volatility-aware trailing framework.
Indicador
W & M Pattern | 3 Peaks + RR ToolW and MW & M Pattern | 3 Peaks + Liquidity Sweep | RR Tool
This indicator identifies high-probability reversal setups by combining classical market structure analysis with liquidity sweep detection — two concepts widely used in Smart Money and Price Action trading.
How It Works
The indicator continuously scans the chart for two mirror-image setups:
Bullish W Pattern (Long Setup)
In a falling market, price forms three consecutive Lower Highs (LH1 → LH2 → LH3), confirming a bearish structure. The indicator then watches for a W formation — where price first drops to a swing low, sweeps below it to grab liquidity (the sharp wick down), and then reverses sharply upward forming the right leg of the W. This liquidity sweep is the key trigger, as it signals that smart money has absorbed sell-side orders and a reversal is likely. A long entry is signaled as price recovers, with the stop loss placed just below the W's sweep low and the take profit targeting either the 1st or 3rd Lower High.
Bearish M Pattern (Short Setup)
In a rising market, price forms three consecutive Higher Highs (HH1 → HH2 → HH3), confirming a bullish structure. The indicator then watches for an M formation — where price pushes above the prior swing high to sweep buy-side liquidity (the sharp wick up), then fails and drops below the neckline. This sweep signals that smart money has distributed into retail buying pressure and a reversal downward is likely. A short entry is signaled as price breaks down, with the stop loss just above the M's sweep high and take profit targeting the 1st or 3rd Higher High. Indicador
NLMS Adaptive Trend Filter [BackQuant]NLMS Adaptive Trend Filter
Overview
The NLMS Adaptive Trend Filter is a machine learning inspired trend-following indicator built around one of the most important adaptive filtering algorithms in signal processing: the Normalized Least Mean Squares (NLMS) filter .
Unlike traditional moving averages that use fixed weighting schemes, the NLMS filter continuously learns from incoming market data and updates its internal coefficients in real time. Rather than assuming that price behavior remains constant, the filter attempts to adapt its structure as market conditions evolve.
This approach originates from the field of digital signal processing, where adaptive filters have been used for decades in applications such as:
• Telecommunications
• Radar systems
• Echo cancellation
• Noise reduction
• Speech processing
• Control systems
• Financial signal extraction
The goal of this indicator is to bring one of these adaptive filtering concepts into market analysis by creating a trend model that continually adjusts itself based on prediction error rather than relying on static averaging methods.
Historical Background
The roots of the NLMS filter can be traced back to the work of Bernard Widrow and Ted Hoff in the late 1950s and early 1960s.
While working at Stanford University, they developed what became known as the:
Least Mean Squares (LMS) Algorithm
The LMS algorithm was revolutionary because it provided a computationally simple method for training adaptive systems using gradient descent.
Rather than solving a complex optimization problem all at once, the LMS algorithm updates its weights incrementally after each observation.
The basic concept was:
1. Make a prediction.
2. Measure the prediction error.
3. Adjust the model slightly.
4. Repeat indefinitely.
This idea eventually became one of the foundational concepts behind modern machine learning and online optimization.
Many modern neural networks still rely on the same underlying principle:
Error → Gradient → Weight Update
The LMS algorithm later evolved into several variants, one of the most important being:
Normalized Least Mean Squares (NLMS)
NLMS improves stability by scaling weight updates according to the energy of the input signal.
This prevents learning rates from becoming too aggressive during high-volatility periods and too weak during low-volatility periods.
As a result, NLMS became one of the most widely used adaptive filtering algorithms in engineering.
What Makes NLMS Different From Moving Averages?
Traditional moving averages use predetermined weights.
For example:
Simple Moving Average (SMA)
Every observation receives equal weight.
Example:
20-period SMA
Each bar contributes:
1 / 20 = 5%
regardless of market conditions.
Exponential Moving Average (EMA)
Recent observations receive more weight.
The weighting structure is fixed and never changes.
Weighted Moving Average (WMA)
Uses linearly decreasing weights.
Again, the weighting scheme is fixed.
The problem is that markets do not operate under fixed conditions.
Volatility changes.
Trend persistence changes.
Noise levels change.
Market structure changes.
Yet traditional moving averages continue using the exact same weighting model.
NLMS takes a different approach.
Instead of assigning permanent weights, it learns them dynamically.
The filter constantly asks
"What weighting structure would have predicted the current market best?"
It then updates itself accordingly.
The Core Idea Behind Adaptive Filters
Imagine trying to forecast today's price using the previous 20 bars.
A normal moving average assumes a fixed weighting pattern.
An adaptive filter attempts to learn the optimal weighting pattern.
At every bar:
• A prediction is generated.
• Actual price is observed.
• Prediction error is measured.
• Weights are adjusted.
The process repeats indefinitely.
Over time, the filter learns which historical observations are most useful and which are less important.
Understanding Filter Taps
One of the most important concepts in adaptive filtering is the idea of:
Taps
A tap is simply a historical observation used as an input.
If the indicator uses:
20 taps
it means:
Price
Price
Price
...
Price
are all being used to generate the prediction.
Each tap receives a learned weight.
Instead of:
Current Estimate =Average of past 20 bars
the filter becomes:
Current Estimate =
(w1 × Price ) +
(w2 × Price ) +
(w3 × Price )
...
(w20 × Price )
The weights are continuously adjusted through learning.
How Prediction Works
The indicator attempts to estimate current price using previous observations.
Mathematically:
Prediction = Σ(weight × historical price)
This prediction becomes the filter output.
If the prediction is accurate:
Weights change very little.
If the prediction is poor:
Weights adjust more aggressively.
This allows the model to gradually adapt to changing market conditions.
Prediction Error
The engine measures:
Error = Actual Price − Predicted Price
This error drives all learning.
Large error means:
The model is wrong.
Small error means:
The model is performing well.
The objective is to minimize prediction error over time.
The LMS Learning Rule
The original LMS update rule is:
New Weight =Old Weight + Learning Rate × Error × Input
This is effectively a form of gradient descent.
The filter moves its weights in the direction that reduces future prediction error.
This is conceptually identical to many machine learning optimization methods.
Why Normalization Matters
The original LMS algorithm has a weakness.
When input values become very large:
Weight updates can become unstable.
This is particularly problematic in financial markets where volatility constantly changes.
NLMS solves this problem by normalizing updates according to signal energy.
Instead of:
Weight Update ∝ Error
it becomes:
Weight Update ∝ Error / Signal Power
This creates adaptive scaling.
When volatility expands:
Updates automatically shrink.
When volatility contracts:
Updates automatically expand.
This improves stability significantly.
How the Indicator Uses NLMS
The script implements an online one-step predictor.
For every new bar:
1. Previous M bars are gathered.
2. Current price is predicted.
3. Prediction error is calculated.
4. Weight vector is updated.
5. New estimate becomes available.
This process occurs continuously as new data arrives.
Because no future data is used, the filter remains fully causal and suitable for live trading.
Weight Initialization
Initially all weights are equal:
1 / M
This effectively starts the model as a simple moving average.
Over time the filter learns a custom weighting structure based on market behavior.
The initial equal-weight state acts as a neutral prior.
Step Size (μ)
The learning rate controls how aggressively the filter adapts.
Lower values:
• More stable
• Smoother output
• Slower adaptation
Higher values:
• Faster adaptation
• More responsiveness
• Greater noise sensitivity
Think of μ as controlling the intelligence speed of the model.
Small values make it conservative.
Large values make it reactive.
Regularization (ε)
Regularization prevents division by very small values.
Without it:
Periods of extremely low signal power could create unstable updates.
Regularization improves numerical stability and robustness.
It acts as a safety mechanism for the learning process.
Output Smoothing
After the NLMS estimate is generated, an optional EMA can be applied.
This smoothing is not part of the NLMS algorithm itself.
It exists purely for visual clarity.
The raw adaptive filter already contains the learning logic.
The smoothing stage simply reduces small fluctuations.
Setting smoothing to 1 effectively disables it.
Trend Detection
Trend direction is derived from the slope of the adaptive filter.
Bullish:
NLMS Output > Previous Output
Bearish:
NLMS Output < Previous Output
This creates a directional state machine.
Unlike crossover systems, trend changes occur whenever the adaptive estimate changes slope.
Bullish Flips
A bullish signal occurs when:
Trend changes from bearish to bullish.
This means the adaptive filter has transitioned from declining to rising.
Bearish Flips
A bearish signal occurs when:
Trend changes from bullish to bearish.
This means the adaptive filter has transitioned from rising to falling.
Visual Components
The indicator includes several visualization layers.
Adaptive Filter Line
The main output of the NLMS model.
This represents the learned trend estimate.
Gradient Fill
The space between price and filter is colorized.
Price Above Filter:
Bullish shading.
Price Below Filter:
Bearish shading.
This provides immediate visual context regarding trend alignment.
Edge Glow
An ATR-based glow surrounds price.
This helps emphasize directional conditions while improving chart readability.
Trend Candles
Candles can optionally inherit trend coloration.
Green:
Adaptive trend rising.
Red:
Adaptive trend falling.
This allows traders to visualize the model's directional state directly on price.
How It Differs From Traditional Trend Filters
Most trend indicators answer:
"What is the average price?"
NLMS attempts to answer:
"What weighting structure best predicts current price?"
This distinction is extremely important.
The indicator is not simply smoothing price.
It is continuously learning how price behaves.
Traditional indicators use fixed mathematics.
NLMS uses adaptive mathematics.
Strengths
• Self-adjusting weighting structure.
• Adapts to changing market conditions.
• Based on established signal-processing theory.
• Stable due to normalization.
• Less reliant on arbitrary moving-average formulas.
• Learns continuously.
• Fully causal and non-lookahead.
Limitations
• Not a predictive model in the forecasting sense.
• Can still lag during major regime shifts.
• Excessively large learning rates may introduce noise.
• Small tap counts can become unstable.
• Large tap counts can become sluggish.
Like all adaptive systems, there is a tradeoff between responsiveness and stability.
Best Use Cases
The NLMS Adaptive Trend Filter is particularly effective for:
• Trend identification.
• Regime classification.
• Dynamic support/resistance visualization.
• Adaptive trend following.
• Noise reduction.
• Signal confirmation.
Summary
The NLMS Adaptive Trend Filter applies one of the most important adaptive algorithms in modern signal processing to financial markets. Rather than relying on fixed moving-average weights, it continuously learns from prediction error and updates its internal model in real time. Built upon the pioneering work of Widrow and Hoff, the indicator combines adaptive filtering, normalized gradient descent, and online learning principles into a practical trend-following tool that evolves alongside changing market conditions. The result is a trend model that is fundamentally different from traditional moving averages, not because it smooths price differently, but because it learns how to smooth price as new information arrives.
Indicador
Indicador
Volatility Gated Supertrend [BackQuant]Volatility Gated Supertrend
Overview
Volatility Gated Supertrend is a regime-aware trend-following indicator built around a modified Supertrend engine with an integrated volatility filter . Unlike a traditional Supertrend, which flips direction whenever price crosses its trailing bands, this version introduces a gating mechanism that can block trend reversals during low-volatility conditions .
The purpose of the indicator is simple:
Keep the responsiveness and structure of a Supertrend.
Reduce false flips during sideways or compressed conditions.
Allow trend transitions primarily when volatility is expanding enough to justify participation.
The result is a smoother and more selective trend engine designed to suppress whipsaws while still reacting to meaningful directional movement.
The full source structure for the indicator can be referenced here: :contentReference {index=0}
Core idea
Traditional Supertrend indicators work well during directional markets but struggle in compressed environments:
Price repeatedly crosses the trailing bands.
Trend direction flips too frequently.
False reversals appear during chop.
This indicator attempts to solve that problem by asking:
“Is there enough volatility expansion to justify accepting a new trend?”
Instead of blindly allowing every flip, the indicator measures:
Current volatility,
Baseline volatility,
Relative expansion or compression.
Only when volatility conditions are sufficient does the trend engine allow a directional transition.
What the Supertrend is
The Supertrend is a volatility-based trailing trend indicator built from:
ATR (Average True Range)
A central price source
A directional trailing stop structure
The classic logic:
Upper band = price source + ATR × multiplier
Lower band = price source − ATR × multiplier
These bands trail price dynamically:
In bullish conditions, the lower band ratchets upward.
In bearish conditions, the upper band ratchets downward.
When price crosses one of the bands:
The trend flips direction.
This creates a clean directional regime model.
How this version differs
The major difference is the volatility gate .
A normal Supertrend asks:
“Did price cross the band?”
This indicator asks:
“Did price cross the band, and is volatility strong enough to trust the move?”
That additional filter dramatically changes behavior in sideways conditions.
ATR and volatility structure
The indicator uses two ATR measurements:
Fast ATR → current short-term volatility
Slow ATR → baseline long-term volatility
The core ratio:
Volatility Ratio = Fast ATR / Slow ATR
Interpretation:
Ratio above threshold → volatility expansion
Ratio below threshold → volatility compression
This becomes the gate logic.
Volatility Gate Logic
The gate opens only when:
Fast ATR / Slow ATR ≥ Gate Threshold
If volatility is too compressed:
The gate closes.
Trend flips are blocked.
Importantly:
The Supertrend bands still calculate normally.
Price can still cross them.
But the directional state will not update while the gate is closed.
This distinction matters because it means:
The market may technically trigger a reversal,
But the indicator intentionally ignores it if volatility conditions are weak.
Why this helps
Most trend-following systems fail in chop because:
Small meaningless moves trigger directional flips.
There is insufficient range expansion.
The market lacks trend persistence.
By requiring volatility confirmation:
Weak reversals are filtered out.
Trend state becomes more stable.
Noise is reduced.
This makes the indicator particularly useful during:
Low-volatility consolidations,
Mean-reverting conditions,
Slow drifting ranges.
Band construction
The indicator uses:
hl2 as the central source,
ATR for dynamic width,
A configurable multiplier for sensitivity.
Formulas:
Upper Band = hl2 + ATR × multiplier
Lower Band = hl2 − ATR × multiplier
The trailing logic prevents the bands from moving backward unnecessarily:
Bullish lower band only rises.
Bearish upper band only falls.
This creates the staircase-style trailing structure common in Supertrend systems.
Trend state
Trend direction is binary:
1 = bullish
-1 = bearish
A raw bullish flip occurs when:
Close > trailing upper band
A raw bearish flip occurs when:
Close < trailing lower band
However:
The trend only updates if the volatility gate is open.
This is the defining behavior of the script.
Blocked flips
One of the most important features is the visualization of blocked signals .
When:
Price crosses a band,
But volatility is insufficient,
The script:
Plots an X-cross marker,
Keeps the existing trend state,
Refuses the flip.
This gives traders visibility into:
Potential but unconfirmed reversals,
Areas of weak participation,
Fake breakouts or low-energy transitions.
Visual behavior
Trend band
The active trailing band changes color based on trend direction:
Bullish → bullish color
Bearish → bearish color
Gate closed → gated color (dimmed)
Trend fill
The script fills the space between price and the active band:
Bullish fill during bullish regimes
Bearish fill during bearish regimes
This creates a cleaner directional overlay.
Outer glow
An additional glow layer expands slightly beyond the trend band:
Adds directional emphasis,
Improves trend readability,
Visually reinforces active regime.
When the gate closes:
The band and candles dim.
This visually communicates:
“The trend engine is currently suppressing flips.”
Candle coloring
Candles can optionally inherit the trend state:
Bullish regime → bullish candles
Bearish regime → bearish candles
Gate closed → dimmed neutral appearance
This allows the indicator to function as a full-chart regime overlay.
Signal logic
Bullish signal
Occurs when:
Trend flips from bearish to bullish,
AND the gate is open.
Bearish signal
Occurs when:
Trend flips from bullish to bearish,
AND the gate is open.
Blocked signal
Occurs when:
A raw flip condition appears,
BUT volatility ratio is below threshold.
This distinction is important:
A blocked signal is not ignored information.
It is a rejected transition.
How to interpret the gate
Gate open
Volatility is active.
Market expansion is sufficient.
Trend flips are allowed.
Gate closed
Market is compressed.
Conditions are likely choppy.
Trend reversals are suppressed.
This effectively turns the indicator into a:
Trend-following system during expansion,
Trend-holding system during compression.
Why ATR ratio works well
ATR ratio is a powerful regime detector because it measures:
Current volatility relative to normal volatility.
Not just:
“Is volatility high?”
But:
“Is volatility high relative to its recent baseline?”
This adaptive behavior allows the gate to work across:
Different assets,
Different timeframes,
Different volatility environments.
Input guide
ATR Multiplier
Controls band width:
Higher = wider bands, fewer flips
Lower = tighter bands, more sensitivity
ATR Length
Controls volatility calculation for the Supertrend itself.
Fast ATR
Short-term volatility measure.
Slow ATR
Long-term baseline volatility measure.
Gate Threshold
Controls how strict the gate is:
Lower threshold = more permissive
Higher threshold = more restrictive
Example:
0.6 → allows more flips
1.0 → requires current volatility to match baseline
1.2 → requires expansion regime
Strengths
Reduces Supertrend whipsaws in chop.
Adds regime awareness.
Uses adaptive volatility filtering.
Clean trend visualization.
Blocked-signal logic provides extra context.
Limitations
Can delay reversals during early expansion.
Very high thresholds may suppress legitimate transitions.
Still fundamentally a trend-following system.
Not designed for low-volatility mean reversion trading.
Best use case
Volatility Gated Supertrend works best as:
A directional regime filter,
A swing trend overlay,
A volatility-aware trend confirmation tool,
A way to suppress noise during consolidations.
It is particularly useful for traders who:
Like Supertrend logic,
But dislike how often it flips in sideways markets.
Summary
Volatility Gated Supertrend extends the classic Supertrend framework by introducing a volatility-aware gating engine that blocks trend reversals during compressed market conditions. By comparing fast ATR against slow ATR, the script determines whether enough volatility expansion exists to justify a directional transition. The result is a cleaner, more stable trend system that retains the strengths of Supertrend logic while dramatically reducing whipsaws during low-energy market regimes. Indicador
Volatility Hull Ribbon [BackQuant]Volatility Hull Ribbon
Overview
Volatility Hull Ribbon is a trend-following overlay built from a Hull-style moving average that replaces traditional volume weighting with volatility weighting . Instead of weighting price by traded volume, this indicator weights price by the absolute True Range of each bar, meaning bars with larger range expansion have more influence on the final trend estimate.
The goal is to create a smoother but responsive trend line that pays more attention to bars where the market actually moved with force. It then plots this volatility-weighted Hull structure as either a clean line or a ribbon-style band, with gradient fill, candle coloring, and long/short flip markers.
At a high level, the indicator does three things:
Builds a volatility-weighted moving average using True Range as the weighting source.
Applies Hull-style lag reduction to produce a faster trend-following curve.
Visualizes trend direction using slope, ribbon fill, candles, and flip signals.
Core idea
Most moving averages treat each bar equally or weight only by time. That means a quiet candle and a high-range expansion candle can have similar influence depending on the MA type.
Volatility Hull Ribbon takes a different approach:
Bars with larger True Range are treated as more important.
Bars with smaller True Range have less influence.
Recent bars are also weighted more heavily than older bars.
This creates a trend estimate that responds more strongly when the market expands, while remaining smoother during lower-energy movement.
What “volatility-weighted” means here
The custom weighting function uses:
Price source
Absolute True Range
A decreasing time weight
For each bar inside the lookback:
Weighted price contribution = source * abs(True Range ) * recency weight
Weight contribution = abs(True Range ) * recency weight
Then:
Volatility-weighted average = weighted price sum / weighted True Range sum
So price movement on wide-range bars matters more than price movement on quiet bars.
Why True Range is used
True Range captures more than just high-low movement. It accounts for gaps and previous close displacement. This makes it a broader volatility proxy than simple candle range.
Using True Range as the weight means the filter gives more importance to bars where:
Range expanded,
Price displaced aggressively,
Volatility increased,
Market participation likely intensified.
This is useful because strong trend moves often occur during volatility expansion, not during quiet drift.
Hull-style construction
The indicator then applies a Hull-style transformation to the volatility-weighted average.
The structure is:
VWHMA = VWMA_TR( 2 * VWMA_TR(src, len / 2) - VWMA_TR(src, len), sqrt(len) )
Where VWMA_TR means the custom True-Range-weighted moving average.
This follows the same logic as the classic Hull Moving Average:
Use a faster half-length average.
Use a slower full-length average.
Subtract the lagging component.
Smooth the result with sqrt(length).
The difference is that every smoothing step is volatility-weighted instead of standard weighted-average based.
Why this matters
A classic Hull Moving Average is already designed to reduce lag. This version modifies the internal weighting so the curve becomes more sensitive to volatility-backed price movement .
That means:
Large expansion bars can pull the filter faster.
Weak low-range chop has less effect.
Trend changes during strong movement can be reflected more clearly.
Trend detection
Trend direction is based on the slope of the VWHMA:
Bullish when VWHMA > VWHMA
Bearish when VWHMA < VWHMA
This is a simple but effective regime definition:
Rising volatility-weighted Hull = bullish trend pressure.
Falling volatility-weighted Hull = bearish trend pressure.
The script uses this slope state to color:
The main line,
The ribbon fill,
Optional candles,
Signal markers.
Ribbon mode
When “Plot as Band?” is enabled, the script creates a second line:
onebar_off = WMA(VWHMA , 10)
This is a delayed and smoothed version of the VWHMA. The area between the current VWHMA and this offset line becomes the ribbon.
Interpretation:
Ribbon expansion shows separation between current trend structure and its delayed reference.
Ribbon compression shows trend slowing or flattening.
A clean flip in the ribbon often coincides with trend transition.
The ribbon is not a volatility band. It is a trend displacement ribbon built from the difference between the current VWHMA and its delayed smoothed version.
Gradient fill logic
The fill is directional:
If VWHMA is above the offset line, fill intensity is stronger near the VWHMA and fades toward the offset.
If VWHMA is below the offset line, the gradient reverses.
This creates a cleaner visual than a flat fill because it emphasizes the active side of the ribbon.
In practice:
Strong bright ribbon = trend line leading the delayed reference.
Faded/narrow ribbon = weaker separation.
Ribbon reversal = trend pressure has shifted.
Signal logic
Signals are generated when the VWHMA slope changes direction:
Long signal: crossover(VWHMA, VWHMA )
Short signal: crossunder(VWHMA, VWHMA )
This means:
A long signal prints when the current VWHMA turns upward relative to the previous value.
A short signal prints when the current VWHMA turns downward.
These are slope-flip signals, not price crossover signals.
Important interpretation
A signal does not mean “buy blindly” or “sell blindly.” It means the volatility-weighted trend estimate has changed direction. The quality of the signal depends on:
Market structure,
Higher timeframe trend,
Volatility conditions,
Whether the ribbon is expanding or compressing.
Candle coloring
When enabled, candles are painted according to the VWHMA slope:
Bullish slope = long color.
Bearish slope = short color.
This makes the indicator easier to read as a regime overlay. You can quickly see when the market is consistently aligned with the volatility-weighted trend.
How to use it
1) Trend filter
Use the VWHMA color as a bias filter:
Only favor longs when the VWHMA is rising.
Only favor shorts when the VWHMA is falling.
2) Trend transition tool
Slope flips can identify early trend shifts:
Long marker = VWHMA has turned upward.
Short marker = VWHMA has turned downward.
Because the filter is Hull-style and volatility-weighted, it can react faster than slower trend filters while still suppressing some low-range noise.
3) Ribbon strength reading
The ribbon gives additional context:
Expanding ribbon = stronger separation and cleaner trend pressure.
Contracting ribbon = momentum weakening.
Ribbon flattening = chop or transition risk.
4) Pullback structure
In strong trends, price often respects the VWHMA or ribbon area:
Bull regime: pullbacks into the ribbon can act as support.
Bear regime: rallies into the ribbon can act as resistance.
5) Volatility-backed trend confirmation
Because large True Range bars influence the calculation more, this tool is useful for identifying whether trend changes are being supported by actual range expansion.
If price moves but the VWHMA does not respond strongly, the move may lack volatility-backed confirmation.
Input guide
Price Source
Defines the input series used for the calculation. Close is standard, but hl2, hlc3, or ohlc4 can be used for smoother structural behavior.
Lookback Period
Controls the smoothing length:
Lower values = faster response, more signals, more noise.
Higher values = smoother trend, fewer flips, more lag.
Plot as Band
Enables the ribbon view using the delayed smoothed VWHMA reference.
Line Width
Controls the main line thickness when not relying heavily on band mode.
Show Trend Candles
Paints candles by current trend state.
Show Signals
Toggles the long/short slope-flip markers.
Strengths
Uses volatility-weighted smoothing instead of equal weighting.
Combines volatility sensitivity with Hull-style lag reduction.
Clean ribbon visualization for trend displacement.
Simple slope-based regime interpretation.
Works well as a trend overlay or bias filter.
Limitations
Slope flips can still whipsaw in sideways markets.
Large wick bars can influence the filter strongly because True Range is used as weight.
It does not measure volume, despite using a VWMA-style internal function.
It is a trend tool, not a complete trading system.
Best use case
Volatility Hull Ribbon works best when used as a visual trend structure layer:
Use color for bias.
Use ribbon expansion/compression for strength.
Use slope flips for regime transitions.
Use price interaction with the ribbon for pullback context.
Summary
Volatility Hull Ribbon is a Hull-style trend overlay that replaces traditional weighting with True Range weighting, making the moving average more responsive to volatility-backed price movement. It builds a low-lag volatility-weighted Hull curve, compares it to a delayed smoothed reference to form a ribbon, and uses slope changes to define trend direction and signals. The result is a clean, responsive trend ribbon that highlights when volatility-backed trend pressure is rising, fading, or reversing. Indicador
Measured Move Projection Zones [AGPro Series]Measured Move Projection Zones
🔹 OVERVIEW
Measured Move Projection Zones is a premium price-action visualization tool built around one clear sequence: impulse, base, projection, and invalidation.
The script detects a qualified impulse leg, waits for a compact base range, then projects a measured-move target band from the base boundary. It also displays invalidation context, event labels, and a compact AGPro panel so the structure can be reviewed quickly on the chart.
The default profile is tuned for 1-hour charts, where measured-move structures need enough responsiveness to appear consistently while still avoiding low-quality micro-swings. The result is a clean projection map for traders who want structured continuation context without turning the chart into a dense extension grid.
This script is not designed to promise outcomes or mark every possible target. It is designed to make the measured-move workflow easier to see, compare, and audit.
🔹 WHAT MAKES IT DIFFERENT
Most projection tools start from a manual anchor, a generic extension grid, or a simple breakout distance. Measured Move Projection Zones is more selective.
It requires a directional impulse first. It then waits for a compact base. Only after the base qualifies does it create the projected target band and invalidation framework.
That sequence matters because it prevents the chart from becoming a collection of random forward boxes. The visual logic is always tied to a specific price-action chain:
Impulse leg -> base range -> projection band -> invalidation context.
The script also avoids the look of a traditional support/resistance map. The rectangles are not generic zones. They represent measured-move components: impulse body, base range, projected target band, and invalidation reference.
For public TradingView presentation, the script is deliberately visual but controlled: moderated labels, visible structure boxes, no expired-label flood, and a compact panel that summarizes the current state.
🧭 WHY THIS DOES NOT OVERLAP WITH OTHER AGPRO TOOLS
This script stays in a narrow measured-move projection lane.
It does not overlap with ATR compression or volatility-map scripts because the core logic is not volatility contraction, expansion, or envelope behavior. ATR is only used for normalization, tolerance, and spacing.
It does not overlap with breakout-quality tools because it does not score a breakout event as the main product. Breakout beyond the base boundary only changes the measured-move state from armed to active.
It does not overlap with premium/discount or valuation-zone tools because it does not map equilibrium, discount, OTE, rebalance pockets, or fair value areas. Its target band is derived from an impulse leg and base boundary, not a valuation model.
It does not overlap with wedge, reversal, or pattern-scanner tools because it does not require converging rails, neckline behavior, double tops, double bottoms, head-and-shoulders logic, or multi-pattern classification.
It does not overlap with liquidity heatmap, bias dashboard, or volume-profile tools because it does not estimate liquidity fields, higher-timeframe directional bias, POC gravity, acceptance ladders, or volume shelves.
The differentiator is simple and specific: this is an impulse-base measured-move projection visualizer with target-band and invalidation context.
⚙️ METHODOLOGY
The methodology is built in stages:
1. Swing Confirmation
The script uses pivot confirmation to identify meaningful swing points. The default pivot setting is tuned for 1-hour chart rhythm.
2. Impulse Qualification
After a valid pivot sequence appears, the script measures the leg size in ATR units. The impulse must be large enough and must form within a reasonable bar window.
3. Base Validation
Once the impulse is confirmed, the script waits for a compact base range. The base must stay within a defined ATR height and avoid excessive retracement from the impulse end.
4. Projection Construction
When the base qualifies, the script projects a measured-move target band from the base boundary. The default multiplier is 1.00, representing a classic equal measured move.
5. Invalidation Context
The opposite side of the base receives an ATR-buffered invalidation guide. This does not create a trade command; it simply marks where the measured-move structure is no longer clean.
6. State Tracking
The setup moves through clear states: Waiting, Building Base, Armed, Projecting, Target Band, Invalidated, and Expired.
7. Visual Management
The script keeps a moderated amount of historical structure visible. Event labels are capped, expired labels are disabled by default, and the projection guide line is optional to keep the chart clean.
📊 PANEL
The AGPro panel is designed for quick structure review.
Panel rows include:
- State
- Direction
- Impulse Quality
- Projection Progress
- Target Distance
- Target Band
- Base Range
- Invalidation
The first panel row follows the AGPro public-release standard: one merged blue header row containing only the panel title.
Panel location is adjustable. Panel theme is adjustable. Panel font size is adjustable. The default size is Normal for a clean public-chart look.
🎛️ KEY INPUTS
1H Pivot Confirmation Length
Controls the swing confirmation used to anchor impulse legs. Lower values are more responsive. Higher values are more selective.
1H Minimum Impulse Size
Defines the minimum impulse strength in ATR units. The default is tuned to keep 1-hour charts active without accepting very small swings.
1H Base Range Bars
Controls how many bars are used to validate the post-impulse base. The default is shorter for hourly chart pacing.
1H Maximum Base Height
Limits how tall the base can be in ATR terms. This prevents wide ranges from being treated as clean measured-move bases.
1H Maximum Base Retracement
Controls how deeply price can retrace from the impulse end while still qualifying as a measured-move structure.
Measured Move Multiplier
Controls the projection distance. The default value of 1.00 represents an equal measured move.
1H Target Band Width
Controls the ATR-based visual tolerance around the projected target.
Invalidation Buffer
Places the invalidation guide beyond the opposite side of the base range.
1H Projection Bars
Controls how far the projected target band and base extension reach forward.
1H Projection Expiration
Controls how long an armed or active projection can remain open before it expires.
1H Event Label Retention
Controls whether the chart keeps a moderated history of event labels or only the latest event label.
1H Balanced Event Labels
Caps event labels so the chart remains informative but not overloaded.
Show Projection Guide Line
Optional dotted guide from the base boundary to the target band. Disabled by default on 1-hour charts to reduce diagonal clutter.
🔍 HOW TO READ IT
Waiting
No valid impulse-base sequence is active.
Building Base
An impulse has been detected and the script is watching for a compact base.
Armed
A valid base has formed. The projection framework is ready, and the target band is mapped forward.
Projecting
Price has moved beyond the base boundary and the measured-move structure is active.
Target Band
Price has interacted with the projected target band.
Invalidated
Price has closed beyond the invalidation guide, meaning the measured-move framework is no longer clean.
Expired
The projection did not complete within the selected expiration window.
Event labels provide a fast visual timeline. The boxes show where the measured structure came from, where the base formed, and where the projected band sits.
🧩 BEST USE CASES
This script is best used on 1-hour charts where traders want a clean view of impulse-base-continuation behavior.
Strong use cases include:
- Measuring continuation structures after a directional leg
- Comparing active projections against nearby price action
- Reviewing whether a base is compact enough to support a projection
- Mapping projected target zones without using a full extension grid
- Studying failed measured moves through invalidation labels and zones
- Creating cleaner screenshots for price-action review
The script can also be used on other timeframes, but the default settings were intentionally tuned around 1-hour structure density and visual balance.
🧠 VISUAL DESIGN PHILOSOPHY
The visual design is built around premium restraint.
The chart should not look empty, but it also should not look like every candle is receiving a signal. Measured Move Projection Zones keeps the main structural elements visible:
- Impulse boxes
- Base range boxes
- Projected target bands
- Invalidation zones or guides
- Moderated event labels
- Compact AGPro panel
Expired labels are disabled by default because they can quickly become noisy on hourly charts. Event labels are still preserved in a moderated amount so the chart has enough visual context.
The optional projection guide line is disabled by default because long diagonal lines can dominate a 1-hour screenshot. Users can enable it when they want a more explicit projection path.
The goal is a chart that looks structured, premium, and publication-ready while still being easy to read.
🔔 ALERTS
The script includes alert conditions for the core lifecycle events:
- Measured Move Armed
- Projection Active
- Target Band Interaction
- Projection Invalidated
- Projection Expired
These alerts are designed around structure states, not trade commands. They help users monitor when a measured-move framework forms, activates, interacts with the projected band, invalidates, or expires.
🔹 LIMITATIONS AND TRANSPARENCY
Measured Move Projection Zones is a structural visualization tool. It does not predict future price and does not claim that a projected target band will be reached.
Pivot-based swing logic confirms structure after the necessary bars have formed. This creates cleaner anchors, but it also means the script is not trying to label every move in real time before confirmation.
The target band is a measured projection derived from the impulse and base, not a certainty zone. Invalidation and expiration states are part of the design because failed measured moves are also useful information.
Settings matter. More aggressive inputs will create more structures. More conservative inputs will create fewer, cleaner structures.
✅ IDEAL USER
This script is ideal for traders who:
- Use 1-hour charts for price-action review
- Study impulse-base-continuation behavior
- Want measured-move target zones without a cluttered extension grid
- Prefer visual structure over heavy signal text
- Want a clean AGPro-style panel for quick state review
- Care about invalidation and failed projection context
- Need a public-chart-friendly tool that looks polished, focused, and easy to understand
Measured Move Projection Zones is built for users who want a disciplined projection framework on the chart: enough structure to be useful, enough restraint to stay premium. Indicador
1-2-3 Reversal Map [AGPro Series]1-2-3 Reversal Map
🔹 OVERVIEW
1-2-3 Reversal Map is a focused TradingView overlay built for traders who want a clean, structured way to follow one of the most recognizable reversal formations in price action: the confirmed 1-2-3 reversal.
This tool maps the full life cycle of a 1-2-3 structure. It identifies the confirmed swing sequence, marks Point 1, Point 2, and Point 3, projects the neckline from Point 2, evaluates the neckline break, and highlights the retest pocket after confirmation. The goal is not to fill the chart with generic reversal signals. The goal is to make the actual 1-2-3 process easier to see, compare, and track.
The script is designed around visual clarity. The latest active structure stays readable through numbered swing labels, restrained guide lines, a clearly identified neckline, and a concept-specific retest pocket. The panel then summarizes the current stage, neckline status, retest status, and reversal score in a compact AG Pro layout.
🔹 WHAT MAKES IT DIFFERENT
Most reversal tools try to do too many things at once. They mix candle patterns, double tops, double bottoms, head and shoulders structures, failed breakouts, generic support and resistance zones, trend filters, and broad reversal markers into one crowded chart.
1-2-3 Reversal Map takes a more disciplined approach. It stays inside one lane: the confirmed 1-2-3 reversal sequence.
The script does not mark every possible turning point. It waits for a defined swing chain:
1. Point 1 establishes the original swing extreme.
2. Point 2 forms the neckline reference.
3. Point 3 confirms that price has created a structurally relevant retracement.
4. The neckline break turns the structure from a setup into a confirmed map.
5. The retest pocket shows where the broken neckline can be evaluated again.
This creates a cleaner workflow than broad reversal scanners. Instead of asking the chart to show everything, the script asks one focused question: has a valid 1-2-3 structure progressed from swing formation to neckline break and retest behavior?
🧭 WHY THIS DOES NOT OVERLAP WITH OTHER AGPRO TOOLS
This script was intentionally built to avoid overlapping with other AGPro public tools.
It is not a broad reversal pattern scanner. It does not combine double top, double bottom, head and shoulders, inverse head and shoulders, wedge, or candle-pattern logic. It focuses only on the 1-2-3 reversal sequence.
It is not a Turtle Soup or failed-breakout tool. It does not begin with a failed range break or liquidity sweep. Its starting point is a confirmed three-point swing structure.
It is not a wedge reversal tool. It does not evaluate converging trendlines, compression geometry, or wedge breakout behavior.
It is not a generic support and resistance map. The rectangle is not a general zone engine. It is a neckline retest pocket that appears only after a valid 1-2-3 neckline break.
It is not a breakout dashboard. Breakout logic exists only as one stage inside the 1-2-3 reversal process.
This makes the script narrow enough for a differentiated AGPro release while still being visually useful and searchable for traders who specifically look for 1-2-3 reversal structure, neckline break, and retest confirmation workflows.
⚙️ METHODOLOGY
The script uses confirmed pivot structure to define each 1-2-3 sequence.
For a bullish 1-2-3 structure:
- Point 1 is a confirmed swing low.
- Point 2 is the recovery swing high and neckline reference.
- Point 3 is a higher low that holds above Point 1.
- The neckline break requires price to close beyond Point 2 with a configurable ATR buffer.
- The retest pocket is projected around the broken neckline after confirmation.
For a bearish 1-2-3 structure:
- Point 1 is a confirmed swing high.
- Point 2 is the reaction swing low and neckline reference.
- Point 3 is a lower high that holds below Point 1.
- The neckline break requires price to close beyond Point 2 with a configurable ATR buffer.
- The retest pocket is projected around the broken neckline after confirmation.
The reversal score is structure-native. It evaluates:
- P1-P2 leg size relative to ATR
- Point 3 hold quality
- P3 retracement balance
- Timing symmetry between structure legs
- Break distance beyond the neckline
- Break candle body quality
- Close location inside the break candle
- Optional volume participation
The score is not designed as a prediction model. It is a ranking layer for comparing the quality of structures that meet the script's own rules.
📊 PANEL
The AG Pro panel is built to keep the structure status readable without forcing the user to interpret every chart object manually.
Panel rows:
- Stage: shows whether the structure is waiting, armed, broken, retested, expired, or invalidated.
- Neckline Break: shows whether the neckline has been confirmed.
- Retest: shows whether the retest pocket is inactive, being watched, or held.
- Reversal Score: shows the current 0-100 score and quality grade.
The panel uses the AGPro standard format:
- One merged blue header row
- Only the script name in the first row
- Adjustable panel location
- Adjustable panel theme
- Adjustable panel font size
🎛️ KEY INPUTS
Pivot Left Bars / Pivot Right Bars:
Controls how mature the swing points must be before the 1-2-3 structure can form. Higher values create fewer and cleaner structures. Lower values make the script more responsive.
Minimum P1-P2 Leg ATR:
Filters out small structures by requiring a minimum distance between Point 1 and Point 2.
Minimum Point 3 Hold ATR:
Defines how much Point 3 must hold relative to Point 1. This helps separate valid structural retracements from weak retests of the original extreme.
Minimum / Maximum P3 Retracement:
Controls the acceptable retracement range for Point 3. This prevents both shallow noise and near-failed structures from being accepted too easily.
Neckline Break Buffer ATR:
Adds a configurable buffer beyond the neckline before the break is accepted.
Retest Pocket Width ATR:
Controls the height of the retest pocket around the broken neckline.
Retest Pocket Projection Bars:
Controls how far the pocket is projected forward.
Show Context Tags:
Adds compact labels such as Neckline and Retest Pocket so the visual elements are easier to identify.
Show Recent Structure Traces:
Keeps a small rolling set of recent structure lines and pockets while keeping numbered swing labels focused on the latest active setup.
Label Font Size:
Controls all chart labels, including swing numbers, context tags, and optional event labels.
Panel Font Size:
Controls the AG Pro panel text size separately from chart labels.
🔍 HOW TO READ IT
Start with the numbered swing labels.
Point 1 marks the original structural extreme. Point 2 marks the neckline reference. Point 3 marks the retracement that must hold for the 1-2-3 structure to remain valid.
Next, watch the neckline.
The neckline is the main confirmation level. Before it breaks, the panel shows the structure as armed or waiting. After it breaks, the structure becomes a confirmed 1-2-3 map.
Then watch the retest pocket.
The retest pocket appears around the broken neckline after confirmation. This is the script's key context zone. It helps the user observe whether price can return to the neckline area and hold the structure instead of treating every move after the break as equally important.
Finally, use the panel score as a quality filter.
A high score means the structure has stronger internal balance according to the script's rules. A lower score means the 1-2-3 sequence may still exist, but its structure quality is weaker.
🧩 BEST USE CASES
This script is best suited for:
- Traders who use classic 1-2-3 reversal logic
- Swing traders who want confirmed pivot structure
- Price-action traders who track neckline breaks
- Traders who prefer breakout-retest workflows
- Users who want fewer, clearer chart objects instead of broad reversal scanners
- Multi-timeframe chart review where structure clarity matters
- Public chart sharing where visual cleanliness is important
It can be useful on crypto, forex, indices, equities, and commodities, especially on charts where swing structure and neckline behavior are visually meaningful.
🧠 VISUAL DESIGN PHILOSOPHY
The design goal is clarity through restraint.
The script avoids a crowded signal-board style. It uses numbered labels only for the current active swing structure. It separates the neckline from the retest pocket with distinct visual language. Recent traces are kept limited and softened so they provide context without dominating the chart.
The active neckline is drawn with a stronger accent color. The retest pocket is shown as a clean rectangle around the broken neckline. Structure legs are dotted and restrained, helping the user understand the geometry without overpowering price.
The chart should feel premium, readable, and publication-ready. The indicator is built to support a clean TradingView screenshot rather than create visual noise.
🔔 ALERTS
The script includes alerts for the main 1-2-3 lifecycle events:
- 1-2-3 structure armed
- Bullish 1-2-3 neckline break
- Bearish 1-2-3 neckline break
- 1-2-3 retest pocket held
- 1-2-3 structure invalidated
These alerts are designed around structure progression, not generic reversal marking.
🔹 LIMITATIONS AND TRANSPARENCY
The script uses confirmed pivots, which means swing points appear only after the required right-side confirmation bars. This is intentional. It prioritizes confirmed structure over instant but unstable markings.
The script does not attempt to identify every possible reversal pattern. It does not evaluate macro trend, fundamentals, order flow, news, or external liquidity conditions.
The reversal score is a structured quality model, not a certainty model. It helps compare 1-2-3 structures inside this script's framework, but it does not forecast outcomes.
Retest pockets are contextual areas around the broken neckline. They are not universal support or resistance zones, and they are not designed to replace broader market analysis.
✅ IDEAL USER
This script is ideal for traders who:
- Understand classic 1-2-3 reversal structure
- Prefer confirmed market structure over early noise
- Want a clean neckline and retest workflow
- Value visual clarity and chart discipline
- Use TradingView for structured price-action review
- Want a focused public-free AGPro tool that does one concept well
1-2-3 Reversal Map is built for users who want a focused reversal map, not a crowded reversal scanner.
🔹 RELEASE NOTES
- Initial public release of 1-2-3 Reversal Map .
- Added confirmed Point 1, Point 2, and Point 3 swing mapping.
- Added neckline projection with close-based break confirmation.
- Added breakout retest pocket around the broken neckline.
- Added context tags for Neckline and Retest Pocket.
- Added AG Pro panel with Stage, Neckline Break, Retest, and Reversal Score.
- Added adjustable panel location, panel theme, label size, and panel font size.
- Added recent structure traces with softened historical visuals.
- Added alerts for armed structures, neckline breaks, retest holds, and invalidations. Indicador
Cup and Handle Quality [AGPro Series]Cup and Handle Quality
🧩 OVERVIEW
Cup and Handle Quality is a visual pattern-quality overlay for one of the most recognized continuation structures in technical analysis: the cup and handle.
The script is designed to map the full pattern lifecycle instead of only marking a breakout candle. It studies the left cup rim, the cup base, the right rim recovery, the controlled handle pullback, the breakout behavior, and the measured projection context. The goal is to make cup and handle structures easier to recognize, compare, and explain directly on the chart.
The final visual output is intentionally clear. The detected cup and handle candle ranges are framed with subtle boxes, while thick curved outlines make the formation readable at a glance. The rim line, target line, DEPTH arrow, and MOVE arrow help users understand how the structure is measured, not just where the label appears.
✅ WHAT MAKES IT DIFFERENT
Most public cup and handle tools focus on one of two things: either they draw a simple breakout marker, or they scan aggressively and leave the chart crowded with low-context shapes. Cup and Handle Quality takes a narrower approach.
It combines three layers:
- Structure recognition: left rim, cup base, right rim, and handle low
- Quality scoring: cup symmetry, handle depth, and breakout quality
- Visual education: cup box, handle box, thick pattern outline, rim line, target line, and measurement arrows
This makes the script more than a pattern detector. It is also a visual explanation tool. The chart shows where the cup was detected, where the handle formed, how deep the cup is, and where the measured projection line comes from.
🧭 WHY THIS DOES NOT OVERLAP WITH OTHER AGPRO TOOLS
This script has its own lane inside the AGPro Series.
It is not a flag scanner, wedge detector, triangle breakout module, inside-bar breakout tool, Donchian breakout validator, double-top detector, head-and-shoulders detector, generic support-resistance map, or supply-demand zone script.
Its lane is specifically:
Cup rim recovery -> controlled handle depth -> breakout participation -> measured projection line.
The script focuses on the complete cup and handle lifecycle. It does not try to replace broader breakout engines, market-structure tools, support-resistance tools, liquidity tools, or trend dashboards. The defining feature is the combination of a recognizable cup-and-handle drawing with a quality panel that grades the actual pattern components.
⚙️ METHODOLOGY
The engine builds the pattern from pivot structure. A qualified setup begins with a left rim, moves into a cup low, recovers into a right rim, and then forms a handle pullback after the right rim.
The quality model evaluates:
1. Cup Symmetry
The script compares the two rim areas and measures how balanced the cup is over time. A cleaner return from the cup base into the right rim area produces a stronger symmetry reading.
2. Handle Depth
The handle is measured as a percentage of cup depth. A useful handle should create structure without pulling so deeply that the cup profile loses strength. The input range allows the user to control how strict or flexible the handle requirement should be.
3. Breakout Quality
Breakout quality is calculated from candle behavior and participation context. The script checks distance beyond the rim, candle body efficiency, close location, and relative volume against a configurable baseline.
4. Final Score
The final score combines the structure score and breakout behavior into a compact quality reading. Developing setups can be shown before breakout confirmation, while confirmed breakouts require the breakout quality gate.
📊 PANEL
The AGPro panel displays the main quality dimensions in a compact format:
- Cup Symmetry
- Handle Depth
- Breakout Quality
- Score
The first row follows the AGPro standard with a merged blue title row. Panel location, panel theme, panel font size, and label font size are adjustable from settings.
🎛️ KEY INPUTS
- Pivot Span controls structural sensitivity.
- Minimum Cup Bars defines the shortest accepted cup duration.
- Maximum Cup Bars defines the longest accepted cup duration.
- Maximum Rim Variance % controls how closely the left and right rims must align.
- Minimum Cup Depth ATR filters shallow structures.
- Minimum Handle Depth % filters handles that are too shallow.
- Maximum Handle Depth % filters handles that are too deep.
- Breakout Volume Baseline controls the relative volume comparison.
- Minimum Setup Score controls developing setup visibility.
- Minimum Breakout Quality controls confirmed breakout strictness.
- Minimum Pattern Score controls the final quality gate.
- Show Developing Setup controls pre-breakout visualization.
- Show Cup Path controls the curved cup drawing and cup candle box.
- Show Handle Box controls the detected handle range.
- Show Target Line controls the measured projection line.
- Show Measurement Arrows controls the DEPTH and MOVE explanation arrows.
- Pattern Stroke Width controls the thickness of the cup and handle outlines.
- Target Projection Bars controls how far the measured target line extends.
🔍 HOW TO READ IT
Start with the rim line. This is the reference level the structure must recover into and eventually move beyond.
Then read the cup. The subtle cup box marks the detected candle range, while the thick curved outline helps the formation read visually as a cup instead of a simple V-shaped swing.
Next read the handle. The handle box marks the controlled pullback area after the right rim. The curved handle outline makes the handle easier to recognize without turning it into a generic rectangle pattern.
The DEPTH arrow shows the measured cup depth. The MOVE arrow transfers that depth upward from the rim area. The TARGET line shows the forward measured projection level.
The panel summarizes the same structure numerically. Stronger Cup Symmetry, disciplined Handle Depth, and stronger Breakout Quality combine into the final Score.
🧩 BEST USE CASES
Cup and Handle Quality is best used on liquid symbols and timeframes where swing structure has enough room to develop. It is especially useful for users who want a clean visual map of a classic continuation pattern without filling the chart with unrelated pattern families.
The default settings are tuned for active discovery. Users who want fewer patterns can raise pivot sensitivity or score thresholds. Users who want a more reactive view can lower the score thresholds, while still using the chart visuals to review pattern quality.
🧠 VISUAL DESIGN PHILOSOPHY
The design philosophy is simple: make the pattern understandable without making the chart noisy.
The cup and handle are drawn with thick curved lines because this pattern is visual by nature. Newer users should be able to see the shape immediately. At the same time, the candle boxes keep the drawing grounded in the actual detected structure.
The target is shown as a line rather than a large zone, keeping the projection clean. The DEPTH and MOVE arrows explain the measurement logic without turning the indicator into a crowded education panel. Labels are compact, and the panel is restrained so the chart remains the main focus.
🔔 ALERTS
The script includes an alert condition for confirmed cup and handle breakouts.
Alert name:
Cup and Handle Quality Breakout
Alert message:
Cup and Handle Quality : high-quality cup and handle breakout confirmed on {{ticker}} at {{close}}.
Alerts are tied to confirmed breakout logic, which means the structure, breakout quality, and pattern score must pass the configured gates.
🔹 LIMITATIONS AND TRANSPARENCY
Cup and handle structures are pattern-based and depend on pivot interpretation. Different sensitivity settings can produce different structures on the same chart.
Very noisy markets, illiquid symbols, extreme gaps, and unusually compressed price action can reduce pattern readability. Lower thresholds may produce more setups, but visual review remains important when using any chart-pattern tool.
The thick cup and handle lines are designed as visual guides. The subtle candle boxes identify the detected structure ranges, while the curved outlines make the pattern easier to understand on the chart.
✅ IDEAL USER
This script is built for traders and analysts who want a clean, visual, and structured way to study cup and handle formations.
It is especially useful for:
- Users who want classic chart patterns with a modern quality layer
- Price-action traders who care about structure, handle depth, and breakout behavior
- Chart reviewers who want a clear visual explanation of the setup
- Newer users who benefit from seeing the cup, handle, depth, move, and target drawn directly on the chart
- AGPro users who want a focused cup-and-handle tool that does not overlap with broader breakout or market-structure scripts Indicador
Darvas Box Breakout Quality [AGPro Series]Darvas Box Breakout Quality
🔹 OVERVIEW
Darvas Box Breakout Quality is built for one of the most recognizable and widely searched chart-pattern structures in technical analysis: the Darvas Box.
The script focuses on the full Darvas lifecycle:
Box formation → compression quality → breakout direction → volume support → failed-break behavior.
Instead of treating every horizontal range as support and resistance, this script waits for a Darvas-style structure to form, validates the box by age and volatility-adjusted height, then evaluates how price resolves from that box. The result is a clean chart-pattern workflow designed for traders who want to study rectangular compression and breakout quality without turning the chart into a crowded zone map.
The main visual element is the active Darvas box itself. By default, resolved boxes are removed after breakout so the chart stays focused on the current live structure instead of filling with old rectangles.
🔹 WHAT MAKES IT DIFFERENT
Most box or breakout tools stop at drawing a rectangle or marking the first break beyond a level. Darvas Box Breakout Quality adds structure, scoring, and failure awareness.
Core differentiators:
• Darvas-first structure logic
The rectangle is not a generic support/resistance zone. It comes from a Darvas box formation process built around a fresh seed high, containment, age, and volatility-adjusted box height.
• Compression quality
The script measures whether the box has enough maturity and controlled range behavior before treating it as a meaningful active structure.
• Breakout quality score
Every qualified breakout is evaluated with a 0-100 model that includes compression quality, relative volume, breakout distance, candle body participation, and directional close location.
• Volume confirmation
Breakout labels can require volume support, helping separate stronger participation events from weaker boundary pokes.
• Failed-break tracking
After breakout, the script watches whether price returns back inside the former box within the selected failure window. If it does, the event is marked as a failed break.
• Premium visual restraint
The default chart view uses one active box, compact labels, controlled label spacing, and a compact AGPro panel. The goal is to make the chart informative without making it noisy.
🧭 WHY THIS DOES NOT OVERLAP WITH OTHER AGPRO TOOLS
This script is intentionally separated from the existing AGPro breakout and chart-pattern family.
It is not Inside Bar Breakout Quality, because it does not require a mother bar or inside-bar compression sequence.
It is not Donchian Breakout Quality, because it is not based on rolling channel highs and lows.
It is not Opening Range Breakout logic, because it is not tied to a session-defined range.
It is not Triangle Breakout Quality, because it does not use converging pivot boundaries, apex pressure, or diagonal structure.
It is not Breakout Volume Quality, because volume is only one part of the confirmation model, not the entire concept.
It is not a supply/demand, order-block, or generic support/resistance zone script. The rectangle exists only when the Darvas box formation process supports it.
That distinction matters visually and analytically. On the chart, this script tells a Darvas story: rectangular compression, active box behavior, quality of release, and failed-break review.
⚙️ METHODOLOGY
1. Darvas seed detection
The script looks for a fresh high over the selected lookback period. This high becomes the initial reference for a potential Darvas box.
2. Box formation
After the seed appears, price must spend enough time contained beneath the upper boundary while the lower boundary develops. The box remains in formation until it meets the selected age and height requirements.
3. Volatility normalization
The box height is measured relative to ATR. This helps filter boxes that are too flat to matter or too wide to represent clean compression.
4. Active box state
When the box qualifies, the script displays the active Darvas box and optional midpoint. The box projects forward so the active breakout boundary remains visible while price approaches it.
5. Breakout confirmation
A bullish breakout requires price to resolve above the Darvas top. A bearish breakout requires price to resolve below the Darvas bottom. Users can require close-based confirmation for stricter filtering.
6. Quality score
The breakout score combines:
• Compression quality
• Relative volume support
• ATR-normalized breakout distance
• Candle body participation
• Directional close location
7. Failed-break monitoring
After breakout, the script watches a defined number of bars. If price returns back inside the former Darvas boundary, the failed-break marker is printed.
📊 PANEL
The AGPro panel summarizes the current Darvas environment:
• Box Age
• Compression
• Breakout Side
• Volume Support
• Latest Quality / State
The first panel row follows the AGPro publication standard: one merged blue header row containing only the panel title. Panel location, panel theme, and panel font size are adjustable from settings.
🎛️ KEY INPUTS
Darvas Box Detection
• New High Lookback
• Minimum Box Age
• Maximum Box Age
• ATR Length
• Minimum Box Height ATR
• Maximum Box Height ATR
• Require Close Beyond Box
Breakout Quality
• Volume MA Length
• Volume Support Threshold
• Require Volume Support
• Target Break Distance ATR
• Minimum Breakout Score
• Failed Break Window
Visual Controls
• Show Active Darvas Box
• Show Box Midline
• Show Breakout Labels
• Show Failed Break Markers
• Keep Resolved Box
• Box Projection Bars
• Label Cooldown Bars
• Maximum Visible Labels
• Label Offset ATR
• Label Stack Offset ATR
• Label Font Size
Panel
• Panel Location
• Panel Theme
• Panel Font Size
🔍 HOW TO READ IT
When a Darvas box becomes active, the chart displays the live rectangular structure. The panel shows how old the box is, how compressed it is, and whether the latest environment has breakout direction or volume support.
When price resolves outside the box with enough quality, the chart prints a compact breakout label such as UP 79 or DN 75. The number represents the breakout quality score.
When price fails to hold outside the box and returns back inside during the selected failure window, the script prints a compact failed-break marker such as FAIL UP or FAIL DN.
The best readings come when the box is visually clear, compression is meaningful, and the breakout candle has both directional close quality and volume support.
🧩 BEST USE CASES
• Classic Darvas box formations
• Rectangular range compression
• Box breakout quality review
• Volume-backed breakout confirmation
• Failed-break review after a box release
• Clean chart-pattern study
• Multi-timeframe Darvas structure observation
• Screenshot-friendly public chart analysis
🧠 VISUAL DESIGN PHILOSOPHY
Darvas Box Breakout Quality is designed to look premium through restraint.
The script avoids filling the chart with old boxes by default. It keeps the active Darvas box as the main visual layer, uses short event labels, adds cooldown and stack spacing to reduce overlap, and keeps the panel compact.
This makes the indicator easier to publish, easier to read, and easier to use across different symbols and timeframes.
🔔 ALERTS
The script includes alert conditions for:
• High-quality bullish Darvas breakout
• High-quality bearish Darvas breakout
• Failed bullish Darvas breakout
• Failed bearish Darvas breakout
These alerts follow the same structure-aware logic used by the chart labels.
🔹 LIMITATIONS AND TRANSPARENCY
Darvas box detection is structure-based and depends on the selected lookback, age, and ATR filters. Changing those settings can make the script more selective or more active.
Volume support depends on the quality of the symbol's volume feed. On instruments where volume is less informative, users may prefer to adjust the volume threshold or disable the volume requirement.
The score is a structured description of breakout quality according to the script's internal model. It is designed to help compare Darvas box releases by quality, not to replace the user's broader market context.
✅ IDEAL USER
This script is designed for traders who want a focused Darvas box tool with cleaner structure detection, breakout quality scoring, volume confirmation, failed-break awareness, and a premium chart layout.
It is best suited for users who want the Darvas box itself to remain the main story on the chart. Indicador
Heikin Ashi Trend Zones [AGPro Series]Heikin Ashi Trend Zones
Heikin Ashi Trend Zones is a clean overlay built for traders who like the smoothing behavior of Heikin Ashi but still want to keep the original market candles visible. Instead of repainting the chart with synthetic candles, the script reads the internal Heikin Ashi state in the background and converts it into a focused trend-state layer.
The engine follows four core ideas:
1. Internal HA Side
The script calculates the active Heikin Ashi side from synthetic HA open and close values, then filters weak neutral bodies so the state does not flip on every small candle.
2. HA Streak Quality
The panel tracks how long the current HA side has been active. This helps separate early state changes from mature continuation phases.
3. Optional Transition Zones
When the HA side changes with enough body strength, wick cleanliness, close location, ATR pressure, and prior-state maturity, the script can project a compact rectangular transition zone. This layer is disabled by default so the public chart view stays clean, but it remains available for traders who want to inspect HA changeover corridors.
4. Continuation Quality
Once a HA streak matures, the script scores continuation quality using body strength, wick cleanliness, close location, smoothed HA slope, streak depth, and ATR context. Labels appear only when the continuation score is strong enough and the cooldown rules allow a clean chart presentation.
What makes this script different
- It does not replace real candles with Heikin Ashi candles.
- It does not behave like a generic trend-following dashboard.
- It focuses on HA state transitions, HA streak maturity, and continuation quality.
- Optional transition boxes are concept-native HA corridors, not broad horizontal support/resistance zones.
- Label density is capped with cooldown and maximum visible label controls.
- The panel exposes HA side, streak, transition quality, continuation quality, and ATR context in a compact AGPro layout.
Visual design
The overlay stays restrained:
- A slim trend-state ribbon follows the smoothed HA path.
- Optional transition zones can extend forward as compact rectangles when enabled.
- Continuation labels are offset from candles with ATR spacing.
- Panel location, panel theme, panel font size, and label font size are adjustable.
Suggested usage
Use the script to study whether Heikin Ashi structure is shifting, stabilizing, or continuing while the original candles remain visible. The strongest reads usually come from alignment between a clean HA side, a growing streak, strong continuation quality, and an ATR context that supports the current state.
Default settings are tuned for a balanced public chart view with a clean ribbon and selective continuation labels. Faster traders can reduce smoothing and cooldown values. Swing traders can enable transition zones, increase transition projection, and require higher continuation quality for fewer labels. Indicador
Flag Continuation Zones [AGPro Series]🔷 Flag Continuation Zones
Flag Continuation Zones is a premium bull flag and bear flag continuation engine designed to identify clean continuation structures without turning the chart into a generic breakout scanner.
The script focuses on a classic, highly recognizable price-action sequence:
impulse pole → controlled flag compression → qualified breakout → forward continuation zone
Instead of marking every small consolidation as a flag, the engine validates the structure through pole strength, travel efficiency, flag depth, channel compression, trend alignment, breakout distance, and optional volume participation.
🔷 What Makes This Different
Most flag indicators are visually simple but structurally loose. They often label shallow pauses, random pullbacks, or broad ranges as flags.
Flag Continuation Zones takes a stricter route.
It first requires a validated impulse pole. The move must be large enough relative to ATR and efficient enough to show directional commitment. After that, the script waits for a controlled counter-trend flag window. The flag must remain compact, avoid excessive retracement, and preserve continuation structure before any breakout is accepted.
This creates a chart experience that is more selective, cleaner, and easier to trust visually.
🔷 How The Engine Works
The script evaluates four core stages:
1. Pole Validation
The prior impulse is measured by ATR multiple and path efficiency. This helps separate real directional movement from noisy grinding price action.
2. Flag Compression
After the pole, the script studies the consolidation window. A valid flag must remain inside an acceptable depth and range relative to the pole.
3. Breakout Confirmation
A continuation event is accepted only when price clears the flag boundary with an ATR buffer and, when available, enough volume participation.
4. Continuation Mapping
Accepted structures create a forward rectangular zone, an impulse pole line, a breakout label, and an optional measured-move projection line.
🔷 Visual Design
The visual language is intentionally restrained:
- clean bull and bear flag labels
- rectangular continuation zones
- impulse pole reference lines
- optional measured-move target line
- trend EMA context
- compact AG Pro status panel
- adjustable panel location
- dark and light panel themes
- adjustable label and panel font sizes
The goal is to make the pattern visible and premium without crowding the chart.
🔷 How This Is Different From Other AGPro Tools
This script is not a generic Trend Continuation Quality tool. It is not an abstract continuation scorecard.
It is specifically built around the flag pattern family:
- impulse pole quality
- flag channel compression
- breakout through the flag boundary
- measured-move continuation context
It also avoids overlapping with triangle, consolidation breakout, Donchian breakout, inside-bar breakout, and trendline tools by staying focused on the pole-and-flag structure itself.
🔷 Best Fit
This script is useful for traders who want to scan for cleaner bull flag and bear flag continuation patterns across crypto, forex, stocks, indices, and futures.
It is especially suitable for:
- continuation traders
- breakout traders who want stricter structure
- price-action traders who follow classic chart patterns
- users who prefer rectangular zones and measured-move context
- traders who want fewer but higher-quality labels
🔷 Key Inputs
Important controls include:
- Pole Lookback
- Flag Window
- Minimum Flag Bars
- Minimum Pole ATR Multiple
- Minimum Pole Efficiency
- Maximum Flag Depth
- Maximum Flag Range
- Breakout Buffer
- Volume Confirmation
- Signal Cooldown
- Zone Forward Bars
- Label Font Size
- Panel Location
- Panel Theme
- Panel Font Size
🔷 In One Sentence
Flag Continuation Zones turns the classic bull flag and bear flag pattern into a cleaner, scored, zone-based continuation map built for premium public chart presentation.
Indicador
