MLLossFunctionsLibrary "MLLossFunctions"
Methods for Loss functions.
mse(expects, predicts) Mean Squared Error (MSE) " MSE = 1/N * sum ((y - y')^2) ".
Parameters:
expects : float array, expected values.
predicts : float array, prediction values.
Returns: float
binary_cross_entropy(expects, predicts) Binary Cross-Entropy Loss (log).
Parameters:
expects : float array, expected values.
predicts : float array, prediction values.
Returns: float
Buscar en scripts para "binary"
B3 HL2 Method Candle PainterThis script is similar to the "Hi-Lo" or "Clear" methods of painting bars. Instead of using the tips/edges of the candles like those two, the "(H+L)/2" method uses the change in (high+low)/2 to paint the bars. This gives you some similar results if you were to be binary with the candle coloring. However, my coloring scheme is not entirely binary. There are 5 possible colors:
HL2>LastHigh = Bright Green
HL2LastHL2 = Dull Green
HL2
DataCorrelationLibrary "DataCorrelation"
Implementation of functions related to data correlation calculations. Formulas have been transformed in such a way that we avoid running loops and instead make use of time series to gradually build the data we need to perform calculation. This allows the calculations to run on unbound series, and/or higher number of samples
🎲 Simplifying Covariance
Original Formula
//For Sample
Covₓᵧ = ∑ ((xᵢ-x̄)(yᵢ-ȳ)) / (n-1)
//For Population
Covₓᵧ = ∑ ((xᵢ-x̄)(yᵢ-ȳ)) / n
Now, if we look at numerator, this can be simplified as follows
∑ ((xᵢ-x̄)(yᵢ-ȳ))
=> (x₁-x̄)(y₁-ȳ) + (x₂-x̄)(y₂-ȳ) + (x₃-x̄)(y₃-ȳ) ... + (xₙ-x̄)(yₙ-ȳ)
=> (x₁y₁ + x̄ȳ - x₁ȳ - y₁x̄) + (x₂y₂ + x̄ȳ - x₂ȳ - y₂x̄) + (x₃y₃ + x̄ȳ - x₃ȳ - y₃x̄) ... + (xₙyₙ + x̄ȳ - xₙȳ - yₙx̄)
=> (x₁y₁ + x₂y₂ + x₃y₃ ... + xₙyₙ) + (x̄ȳ + x̄ȳ + x̄ȳ ... + x̄ȳ) - (x₁ȳ + x₂ȳ + x₃ȳ ... xₙȳ) - (y₁x̄ + y₂x̄ + y₃x̄ + yₙx̄)
=> ∑xᵢyᵢ + n(x̄ȳ) - ȳ∑xᵢ - x̄∑yᵢ
So, overall formula can be simplified to be used in pine as
//For Sample
Covₓᵧ = (∑xᵢyᵢ + n(x̄ȳ) - ȳ∑xᵢ - x̄∑yᵢ) / (n-1)
//For Population
Covₓᵧ = (∑xᵢyᵢ + n(x̄ȳ) - ȳ∑xᵢ - x̄∑yᵢ) / n
🎲 Simplifying Standard Deviation
Original Formula
//For Sample
σ = √(∑(xᵢ-x̄)² / (n-1))
//For Population
σ = √(∑(xᵢ-x̄)² / n)
Now, if we look at numerator within square root
∑(xᵢ-x̄)²
=> (x₁² + x̄² - 2x₁x̄) + (x₂² + x̄² - 2x₂x̄) + (x₃² + x̄² - 2x₃x̄) ... + (xₙ² + x̄² - 2xₙx̄)
=> (x₁² + x₂² + x₃² ... + xₙ²) + (x̄² + x̄² + x̄² ... + x̄²) - (2x₁x̄ + 2x₂x̄ + 2x₃x̄ ... + 2xₙx̄)
=> ∑xᵢ² + nx̄² - 2x̄∑xᵢ
=> ∑xᵢ² + x̄(nx̄ - 2∑xᵢ)
So, overall formula can be simplified to be used in pine as
//For Sample
σ = √(∑xᵢ² + x̄(nx̄ - 2∑xᵢ) / (n-1))
//For Population
σ = √(∑xᵢ² + x̄(nx̄ - 2∑xᵢ) / n)
🎲 Using BinaryInsertionSort library
Chatterjee Correlation and Spearman Correlation functions make use of BinaryInsertionSort library to speed up sorting. The library in turn implements mechanism to insert values into sorted order so that load on sorting is reduced by higher extent allowing the functions to work on higher sample size.
🎲 Function Documentation
chatterjeeCorrelation(x, y, sampleSize, plotSize)
Calculates chatterjee correlation between two series. Formula is - ξnₓᵧ = 1 - (3 * ∑ |rᵢ₊₁ - rᵢ|)/ (n²-1)
Parameters:
x : First series for which correlation need to be calculated
y : Second series for which correlation need to be calculated
sampleSize : number of samples to be considered for calculattion of correlation. Default is 20000
plotSize : How many historical values need to be plotted on chart.
Returns: float correlation - Chatterjee correlation value if falls within plotSize, else returns na
spearmanCorrelation(x, y, sampleSize, plotSize)
Calculates spearman correlation between two series. Formula is - ρ = 1 - (6∑dᵢ²/n(n²-1))
Parameters:
x : First series for which correlation need to be calculated
y : Second series for which correlation need to be calculated
sampleSize : number of samples to be considered for calculattion of correlation. Default is 20000
plotSize : How many historical values need to be plotted on chart.
Returns: float correlation - Spearman correlation value if falls within plotSize, else returns na
covariance(x, y, include, biased)
Calculates covariance between two series of unbound length. Formula is Covₓᵧ = ∑ ((xᵢ-x̄)(yᵢ-ȳ)) / (n-1) for sample and Covₓᵧ = ∑ ((xᵢ-x̄)(yᵢ-ȳ)) / n for population
Parameters:
x : First series for which covariance need to be calculated
y : Second series for which covariance need to be calculated
include : boolean flag used for selectively including sample
biased : boolean flag representing population covariance instead of sample covariance
Returns: float covariance - covariance of selective samples of two series x, y
stddev(x, include, biased)
Calculates Standard Deviation of a series. Formula is σ = √( ∑(xᵢ-x̄)² / n ) for sample and σ = √( ∑(xᵢ-x̄)² / (n-1) ) for population
Parameters:
x : Series for which Standard Deviation need to be calculated
include : boolean flag used for selectively including sample
biased : boolean flag representing population covariance instead of sample covariance
Returns: float stddev - standard deviation of selective samples of series x
correlation(x, y, include)
Calculates pearson correlation between two series of unbound length. Formula is r = Covₓᵧ / σₓσᵧ
Parameters:
x : First series for which correlation need to be calculated
y : Second series for which correlation need to be calculated
include : boolean flag used for selectively including sample
Returns: float correlation - correlation between selective samples of two series x, y
Wick Detection (1 and 0) - AYNETDetailed Scientific Explanation
1. Wick Detection Logic
Definition of a Wick:
A wick, also known as a shadow, represents the price action outside the range of a candlestick's body (the region between open and close).
Upper Wick: Occurs when the high value exceeds the greater of open and close.
Lower Wick: Occurs when the low value is lower than the smaller of open and close.
Upper Wick Detection:
pinescript
Kodu kopyala
bool has_upper_wick = high > math.max(open, close)
This checks if the high price of the candle is greater than the maximum of the open and close prices. If true, an upper wick exists.
Lower Wick Detection:
pinescript
Kodu kopyala
bool has_lower_wick = low < math.min(open, close)
This checks if the low price of the candle is less than the minimum of the open and close prices. If true, a lower wick exists.
2. Binary Representation
The presence of a wick is encoded as a binary value for simplicity and computational analysis:
Upper Wick: Represented as 1 if present, otherwise 0.
pinescript
Kodu kopyala
float upper_wick_binary = has_upper_wick ? 1 : 0
Lower Wick: Represented as 1 if present, otherwise 0. This value is inverted (-1) for visualization purposes.
pinescript
Kodu kopyala
float lower_wick_binary = has_lower_wick ? 1 : 0
3. Visualization with Histograms
The plot function is used to create histograms for visualizing the binary wick data:
Upper Wicks: Plotted as positive values with green columns:
pinescript
Kodu kopyala
plot(upper_wick_binary, title="Upper Wick", color=color.new(color.green, 0), style=plot.style_columns, linewidth=2)
Lower Wicks: Plotted as negative values with red columns:
pinescript
Kodu kopyala
plot(lower_wick_binary * -1, title="Lower Wick", color=color.new(color.red, 0), style=plot.style_columns, linewidth=2)
Features and Applications
1. Wick Visualization:
Upper wicks are displayed as positive green columns.
Lower wicks are displayed as negative red columns.
This provides a clear visual representation of wick presence in historical data.
2. Technical Analysis:
Wick formations often indicate market sentiment:
Upper Wicks: Sellers pushed the price lower after buyers drove it higher, signaling rejection at the top.
Lower Wicks: Buyers pushed the price higher after sellers drove it lower, signaling rejection at the bottom.
3. Signal Generation:
Traders can use wick detection to build strategies, such as identifying key price levels or market reversals.
Enhancements and Future Improvements
1. Wick Length Measurement
Instead of binary detection, measure the actual length of the wick:
pinescript
Kodu kopyala
float upper_wick_length = high - math.max(open, close)
float lower_wick_length = math.min(open, close) - low
This approach allows for thresholds to identify significant wicks:
pinescript
Kodu kopyala
bool significant_upper_wick = upper_wick_length > 10 // For wicks longer than 10 units.
bool significant_lower_wick = lower_wick_length > 10
2. Alerts for Long Wicks
Trigger alerts when significant wicks are detected:
pinescript
Kodu kopyala
alertcondition(significant_upper_wick, title="Long Upper Wick", message="A significant upper wick has been detected.")
alertcondition(significant_lower_wick, title="Long Lower Wick", message="A significant lower wick has been detected.")
3. Combined Wick Analysis
Analyze both upper and lower wicks to assess volatility:
pinescript
Kodu kopyala
float total_wick_length = upper_wick_length + lower_wick_length
bool high_volatility = total_wick_length > 20 // Combined wick length exceeds 20 units.
Conclusion
This script provides a compact and computationally efficient way to detect candlestick wicks and represent them as binary data. By visualizing the data with histograms, traders can easily identify wick formations and use them for technical analysis, signal generation, and volatility assessment. The approach can be extended further to measure wick length, detect significant wicks, and integrate these insights into automated trading systems.
Zero-lag Volatility-Breakout EMA Trend StrategyThis is a simple volatility-breakout strategy which uses the difference in two different zero-lag* EMAs (explained below on what exactly I mean by this) to track the upwards or downwards strength of an instrument. When the difference breaks above a Bollinger Band of a configurable standard deviation multiple, the strategy enters based off the direction of the base EMA used (i.e. if the difference breaks above and the current EMA is rising, a long entry is produced. If the difference breaks above and the current EMA is falling, a short entry is produced).
The two EMA-type metrics used to calculate the volatility difference are calculated by the following formula:
top_ema = math.max(src, ta.ema(src, length))
bottom_ema = math.min(src, ta.ema(src, length))
ema_difference = (top_ema - bottom_ema) - 1
This produces a difference which responds immediately to large price movements, instead of lagging if it used strictly the EMA itself.
SETTINGS
Source : The source of the strategy - close, hlc3, another indicator plot, etc.
EMA Difference Length : The length of both the EMA difference statistics and the base EMA used to calculate the entry side.
Standard Deviation Multiple : The Bollinger Bands multiple used when the difference is breaking out.
Use Binary Strategy : The strategy has two configurations: Binary and Rapid-Exit. 'Binary' means that it will not close a long position until a short position is generated, and vice-versa. 'Rapid-Exit' will close a long or short position once the difference reaches the middle Bollinger Band MA. This means that turning on 'Binary' will expose you to more market risk, but potentially greater market return. Turning off 'Binary' will exit quickly and reduce drawdown.
The strategy results below use 10% equity and 0.1% fees per trade.
Qualitative Smoothed Strength Index***RSI CHART BELOW IS FOR COMPARSION TO SHOW HOE THEY MAKE SIMILIAR PATTERNS*** IT IS NOT PART OF THE INDICATOR***
The Qualitative Smoothed Strength Index (QSSI) is a simplified momentum oscillator whose values will oscillate between 0 and 1 . By converting price differences into binary values and smoothing them with a moving average, it identifies qualitative strength of price movements. This simplification allows traders to easily interpret trends and reversals. The QSSI offers advantages such as noise reduction, clear trend identification, and early signal detection, resulting in less lag compared to traditional oscillators. Traders can customize the indicator based on their preferences and use it across various markets.
QSSI Indicator uses the input function is used to define the input parameters of the indicator. In this case, there are two inputs:
length: The number of periods used for calculating the differences (a, b, c) and their assigned values. Default value is 5.
MAL: The length of the moving average used for smoothing the assigned values. Default value is 14.
The next few lines calculate 'a', 'b', and 'c', which represent the differences between the high, low, and close prices, respectively, and their corresponding previous simple moving averages (SMAs) of specified length. These differences are used to identify price movements.
The code assigns binary values (0 or 1) to a_assigned, b_assigned, and c_assigned, depending on whether the corresponding differences (a, b, c) are greater than 0. This step converts the differences into a binary representation, indicating upward or downward price movements.
Average_assigned calculates the average of the assigned binary values of a, b, and c. This average value represents the overall strength of the price movement.ma_assigned calculates the 14-day moving average of average_assigned, which smoothens the indicator and helps traders identify trends more easily.
The code plots the 14-day moving average (ma_assigned) on the chart as a blue line. It also plots the individual assigned values of a, b, and c as dots on the chart. a_assigned is shown in green, b_assigned in red, and c_assigned in black. These dots indicate the presence of upward or downward movements in the respective price components. By visualizing these dots on the chart, the trader can quickly identify the presence and direction of price movements for each of the price components. This information can be valuable for understanding how the different price elements (high, low, and close) are contributing to the overall trend and strength of the market. Traders can use this data to make more informed decisions, such as confirming the presence of trends, identifying potential reversals, or gauging the overall market sentiment based on the distribution of upward and downward movements across the price components.
Finally, the code draws horizontal dotted lines at levels 0.70 (0.8)and 0.30 (0.2). These levels are typically used to identify overbought (above 0.70 or 0.8) and oversold (below 0.30 or 0.2) conditions in the market.
The Qualitative Smoothed Strength Index (QSSI) provides traders with information about the strength and direction of price movements. By using assigned binary values, the indicator simplifies the interpretation of price data, making it easier to identify trends and potential reversals.
MLMatrixLibOverview
MLMatrixLib is a comprehensive Pine Script v6 library implementing machine learning algorithms using native matrix operations. This library provides traders and developers with a toolkit of statistical and ML methods for building quantitative trading systems, performing data analysis, and creating adaptive indicators.
How It Works
The library leverages Pine Script's native matrix type to perform efficient linear algebra operations. Each algorithm is implemented from first principles, using matrix decomposition, iterative optimization, and statistical estimation techniques. All functions are designed for numerical stability with careful handling of edge cases.
---
Library Contents (34 Sections)
Section 1: Utility Functions & Matrix Operations
Core building blocks including:
• identity(n) - Creates n×n identity matrix
• diagonal(values) - Creates diagonal matrix from array
• ones(rows, cols) / zeros(rows, cols) - Matrix constructors
• frobeniusNorm(m) / l1Norm(m) - Matrix norm calculations
• hadamard(m1, m2) - Element-wise multiplication
• columnMeans(m) / rowMeans(m) - Statistical aggregations
• standardize(m) - Z-score normalization (zero mean, unit variance)
• minMaxNormalize(m) - Scale values to range
• fitStandardScaler(m) / fitMinMaxScaler(m) - Reusable scaler parameters
• addBiasColumn(m) - Prepend column of ones for regression
• arrayMedian(arr) / arrayPercentile(arr, p) - Array statistics
Section 2: Activation Functions
Numerically stable implementations:
• sigmoid(x) / sigmoidMatrix(m) - Logistic function with overflow protection
• tanhActivation(x) / tanhMatrix(m) - Hyperbolic tangent
• relu(x) / reluMatrix(m) - Rectified Linear Unit
• leakyRelu(x, alpha) - Leaky ReLU with configurable slope
• elu(x, alpha) - Exponential Linear Unit
• Derivatives for backpropagation: sigmoidDerivative, tanhDerivative, reluDerivative
Section 3: Linear Regression (OLS)
Ordinary Least Squares implementation using the normal equation (X'X)⁻¹X'y:
• fitLinearRegression(X, y) - Fits model, returns coefficients, R², standard error
• fitSimpleLinearRegression(x, y) - Single-variable regression
• predictLinear(model, X) - Generate predictions
• predictionInterval(model, X, confidence) - Confidence intervals using t-distribution
• Model type stores: coefficients, R-squared, residuals, standard error
Section 4: Weighted Linear Regression
Generalized least squares with observation weights:
• fitWeightedLinearRegression(X, y, weights) - Solves (X'WX)⁻¹X'Wy
• Useful for downweighting outliers or emphasizing recent data
Section 5: Polynomial Regression
Fits polynomials of arbitrary degree:
• fitPolynomialRegression(x, y, degree) - Constructs Vandermonde matrix
• predictPolynomial(model, x) - Evaluate polynomial at points
Section 6: Ridge Regression (L2 Regularization)
Adds penalty term λ||β||² to prevent overfitting:
• fitRidgeRegression(X, y, lambda) - Solves (X'X + λI)⁻¹X'y
• Lambda parameter controls regularization strength
Section 7: LASSO Regression (L1 Regularization)
Coordinate descent algorithm for sparse solutions:
• fitLassoRegression(X, y, lambda, maxIter, tolerance) - Iterative soft-thresholding
• Produces sparse coefficients by driving some to exactly zero
• softThreshold(x, lambda) - Core shrinkage operator
Section 8: Elastic Net (L1 + L2 Regularization)
Combines LASSO and Ridge penalties:
• fitElasticNet(X, y, lambda, alpha, maxIter, tolerance)
• Alpha balances L1 vs L2: alpha=1 is LASSO, alpha=0 is Ridge
Section 9: Huber Robust Regression
Iteratively Reweighted Least Squares (IRLS) for outlier resistance:
• fitHuberRegression(X, y, delta, maxIter, tolerance)
• Delta parameter defines transition between L1 and L2 loss
• Downweights observations with large residuals
Section 10: Quantile Regression
Estimates conditional quantiles using linear programming approximation:
• fitQuantileRegression(X, y, tau, maxIter, tolerance)
• Tau specifies quantile (0.5 = median, 0.25 = lower quartile, etc.)
Section 11: Logistic Regression (Binary Classification)
Gradient descent optimization of cross-entropy loss:
• fitLogisticRegression(X, y, learningRate, maxIter, tolerance)
• predictProbability(model, X) - Returns probabilities
• predictClass(model, X, threshold) - Returns binary predictions
Section 12: Linear SVM (Support Vector Machine)
Sub-gradient descent with hinge loss:
• fitLinearSVM(X, y, C, learningRate, maxIter)
• C parameter controls regularization (higher = harder margin)
• predictSVM(model, X) - Returns class predictions
Section 13: Recursive Least Squares (RLS)
Online learning with exponential forgetting:
• createRLSState(nFeatures, lambda, delta) - Initialize state
• updateRLS(state, x, y) - Update with new observation
• Lambda is forgetting factor (0.95-0.99 typical)
• Useful for adaptive indicators that update incrementally
Section 14: Covariance and Correlation
Matrix statistics:
• covarianceMatrix(m) - Sample covariance
• correlationMatrix(m) - Pearson correlations
• pearsonCorrelation(x, y) - Single correlation coefficient
• spearmanCorrelation(x, y) - Rank-based correlation
Section 15: Principal Component Analysis (PCA)
Dimensionality reduction via eigendecomposition:
• fitPCA(X, nComponents) - Power iteration method
• transformPCA(X, model) - Project data onto principal components
• Returns components, explained variance, and mean
Section 16: K-Means Clustering
Lloyd's algorithm with k-means++ initialization:
• fitKMeans(X, k, maxIter, tolerance) - Cluster data points
• predictCluster(model, X) - Assign new points to clusters
• withinClusterVariance(model) - Measure cluster compactness
Section 17: Gaussian Mixture Model (GMM)
Expectation-Maximization algorithm:
• fitGMM(X, k, maxIter, tolerance) - Soft clustering with probabilities
• predictProbaGMM(model, X) - Returns membership probabilities
• Models data as mixture of Gaussian distributions
Section 18: Kalman Filter
Linear state estimation:
• createKalman1D(processNoise, measurementNoise, ...) - 1D filter
• createKalman2D(processNoise, measurementNoise) - Position + velocity tracking
• kalmanStep(state, measurement) - Predict-update cycle
• Optimal filtering for noisy measurements
Section 19: K-Nearest Neighbors (KNN)
Instance-based learning:
• fitKNN(X, y) - Store training data
• predictKNN(model, X, k) - Classify by majority vote
• predictKNNRegression(model, X, k) - Average of k neighbors
• predictKNNWeighted(model, X, k) - Distance-weighted voting
Section 20: Neural Network (Feedforward)
Multi-layer perceptron:
• createNeuralNetwork(architecture) - Define layer sizes
• trainNeuralNetwork(nn, X, y, learningRate, epochs) - Backpropagation
• predictNN(nn, X) - Forward pass
• Supports configurable hidden layers
Section 21: Naive Bayes Classifier
Gaussian Naive Bayes:
• fitNaiveBayes(X, y) - Estimate class-conditional distributions
• predictNaiveBayes(model, X) - Maximum a posteriori classification
• Assumes feature independence given class
Section 22: Anomaly Detection
Statistical outlier detection:
• fitAnomalyDetector(X, contamination) - Mahalanobis distance-based
• detectAnomalies(model, X) - Returns anomaly scores
• isAnomaly(model, X, threshold) - Binary classification
Section 23: Dynamic Time Warping (DTW)
Time series similarity:
• dtw(series1, series2) - Compute DTW distance
• Handles sequences of different lengths
• Useful for pattern matching
Section 24: Markov Chain / Regime Detection
Discrete state transitions:
• fitMarkovChain(states, nStates) - Estimate transition matrix
• predictNextState(transitionMatrix, currentState) - Most likely next state
• stationaryDistribution(transitionMatrix) - Long-run probabilities
Section 25: Hidden Markov Model (Simple)
Baum-Welch algorithm:
• fitHMM(observations, nStates, maxIter) - EM training
• viterbi(model, observations) - Most likely state sequence
• Useful for regime detection
Section 26: Exponential Smoothing & Holt-Winters
Time series smoothing:
• exponentialSmooth(data, alpha) - Simple exponential smoothing
• holtWinters(data, alpha, beta, gamma, seasonLength) - Triple smoothing
• Captures trend and seasonality
Section 27: Entropy and Information Theory
Information measures:
• entropy(probabilities) - Shannon entropy in bits
• conditionalEntropy(jointProbs, marginalProbs) - H(X|Y)
• mutualInformation(probsX, probsY, jointProbs) - I(X;Y)
• kldivergence(p, q) - Kullback-Leibler divergence
Section 28: Hurst Exponent
Long-range dependence measure:
• hurstExponent(data) - R/S analysis
• H < 0.5: mean-reverting, H = 0.5: random walk, H > 0.5: trending
Section 29: Change Detection (CUSUM)
Cumulative sum control chart:
• cusumChangeDetection(data, threshold, drift) - Detect regime changes
• cusumOnline(value, prevCusumPos, prevCusumNeg, target, drift) - Streaming version
Section 30: Autocorrelation
Serial dependence analysis:
• autocorrelation(data, maxLag) - ACF for all lags
• partialAutocorrelation(data, maxLag) - PACF via Durbin-Levinson
• Useful for time series model identification
Section 31: Ensemble Methods
Model combination:
• baggingPredict(models, X) - Average predictions
• votingClassify(models, X) - Majority vote
• Improves robustness through aggregation
Section 32: Model Evaluation Metrics
Performance assessment:
• mse(actual, predicted) / rmse / mae / mape - Regression metrics
• accuracy(actual, predicted) - Classification accuracy
• precision / recall / f1Score - Binary classification metrics
• confusionMatrix(actual, predicted, nClasses) - Multi-class evaluation
• rSquared(actual, predicted) / adjustedRSquared - Goodness of fit
Section 33: Cross-Validation
Model validation:
• trainTestSplit(X, y, trainRatio) - Random split
• Foundation for walk-forward validation
Section 34: Trading Convenience Functions
Trading-specific utilities:
• priceMatrix(length) - OHLC data as matrix
• logReturns(length) - Log return series
• rollingSlope(src, length) - Linear trend strength
• kalmanFilter(src, processNoise, measurementNoise) - Filtered price
• kalmanFilter2D(src, ...) - Price with velocity estimate
• adaptiveMA(src, sensitivity) - Kalman-based adaptive moving average
• volAdjMomentum(src, length) - Volatility-normalized momentum
• detectSRLevels(length, nLevels) - K-means based S/R detection
• buildFeatures(src, lengths) - Multi-timeframe feature construction
• technicalFeatures(length) - Standard indicator feature set (RSI, MACD, BB, ATR, etc.)
• lagFeatures(src, lags) - Time-lagged features
• sharpeRatio(returns) - Risk-adjusted return measure
• sortinoRatio(returns) - Downside risk-adjusted return
• maxDrawdown(equity) - Maximum peak-to-trough decline
• calmarRatio(returns, equity) - Return/drawdown ratio
• kellyCriterion(winRate, avgWin, avgLoss) - Optimal position sizing
• fractionalKelly(...) - Conservative Kelly sizing
• rollingBeta(assetReturns, benchmarkReturns) - Market exposure
• fractalDimension(data) - Market complexity measure
---
Usage Example
```
import YourUsername/MLMatrixLib/1 as ml
// Create feature matrix
matrix X = ml.priceMatrix(50)
X := ml.standardize(X)
// Fit linear regression
ml.LinearRegressionModel model = ml.fitLinearRegression(X, y)
float prediction = ml.predictLinear(model, X_new)
// Kalman filter for smoothing
float smoothedPrice = ml.kalmanFilter(close, 0.01, 1.0)
// Detect support/resistance levels
array levels = ml.detectSRLevels(100, 3)
// K-means clustering for regime detection
ml.KMeansModel km = ml.fitKMeans(features, 3)
int cluster = ml.predictCluster(km, newFeature)
```
---
Technical Notes
• All matrix operations use Pine Script's native matrix type
• Numerical stability ensured through:
- Clamping exponential arguments to prevent overflow
- Division by zero protection with epsilon thresholds
- Iterative algorithms with convergence tolerance
• Designed for bar-by-bar execution in Pine Script's event-driven model
• Compatible with Pine Script v6
---
Disclaimer
This library provides mathematical tools for quantitative analysis. It does not constitute financial advice. Past performance of any algorithm does not guarantee future results. Users are responsible for validating models on their specific use cases and understanding the limitations of each method.
Historical Matrix Analyzer [PhenLabs]📊Historical Matrix Analyzer
Version: PineScriptv6
📌Description
The Historical Matrix Analyzer is an advanced probabilistic trading tool that transforms technical analysis into a data-driven decision support system. By creating a comprehensive 56-cell matrix that tracks every combination of RSI states and multi-indicator conditions, this indicator reveals which market patterns have historically led to profitable outcomes and which have not.
At its core, the indicator continuously monitors seven distinct RSI states (ranging from Extreme Oversold to Extreme Overbought) and eight unique indicator combinations (MACD direction, volume levels, and price momentum). For each of these 56 possible market states, the system calculates average forward returns, win rates, and occurrence counts based on your configurable lookback period. The result is a color-coded probability matrix that shows you exactly where you stand in the historical performance landscape.
The standout feature is the Current State Panel, which provides instant clarity on your active market conditions. This panel displays signal strength classifications (from Strong Bullish to Strong Bearish), the average return percentage for similar past occurrences, an estimated win rate using Bayesian smoothing to prevent small-sample distortions, and a confidence level indicator that warns you when insufficient data exists for reliable conclusions.
🚀Points of Innovation
Multi-dimensional state classification combining 7 RSI levels with 8 indicator combinations for 56 unique trackable market conditions
Bayesian win rate estimation with adjustable smoothing strength to provide stable probability estimates even with limited historical samples
Real-time active cell highlighting with “NOW” marker that visually connects current market conditions to their historical performance data
Configurable color intensity sensitivity allowing traders to adjust heat-map responsiveness from conservative to aggressive visual feedback
Dual-panel display system separating the comprehensive statistics matrix from an easy-to-read current state summary panel
Intelligent confidence scoring that automatically warns traders when occurrence counts fall below reliable thresholds
🔧Core Components
RSI State Classification: Segments RSI readings into 7 distinct zones (Extreme Oversold <20, Oversold 20-30, Weak 30-40, Neutral 40-60, Strong 60-70, Overbought 70-80, Extreme Overbought >80) to capture momentum extremes and transitions
Multi-Indicator Condition Tracking: Simultaneously monitors MACD crossover status (bullish/bearish), volume relative to moving average (high/low), and price direction (rising/falling) creating 8 binary-encoded combinations
Historical Data Storage Arrays: Maintains rolling lookback windows storing RSI states, indicator states, prices, and bar indices for precise forward-return calculations
Forward Performance Calculator: Measures price changes over configurable forward bar periods (1-20 bars) from each historical state, accumulating total returns and win counts per matrix cell
Bayesian Smoothing Engine: Applies statistical prior assumptions (default 50% win rate) weighted by user-defined strength parameter to stabilize estimated win rates when sample sizes are small
Dynamic Color Mapping System: Converts average returns into color-coded heat map with intensity adjusted by sensitivity parameter and transparency modified by confidence levels
🔥Key Features
56-Cell Probability Matrix: Comprehensive grid displaying every possible combination of RSI state and indicator condition, with each cell showing average return percentage, estimated win rate, and occurrence count for complete statistical visibility
Current State Info Panel: Dedicated display showing your exact position in the matrix with signal strength emoji indicators, numerical statistics, and color-coded confidence warnings for immediate situational awareness
Customizable Lookback Period: Adjustable historical window from 50 to 500 bars allowing traders to focus on recent market behavior or capture longer-term pattern stability across different market cycles
Configurable Forward Performance Window: Select target holding periods from 1 to 20 bars ahead to align probability calculations with your trading timeframe, whether day trading or swing trading
Visual Heat Mapping: Color-coded cells transition from red (bearish historical performance) through gray (neutral) to green (bullish performance) with intensity reflecting statistical significance and occurrence frequency
Intelligent Data Filtering: Minimum occurrence threshold (1-10) removes unreliable patterns with insufficient historical samples, displaying gray warning colors for low-confidence cells
Flexible Layout Options: Independent positioning of statistics matrix and info panel to any screen corner, accommodating different chart layouts and personal preferences
Tooltip Details: Hover over any matrix cell to see full RSI label, complete indicator status description, precise average return, estimated win rate, and total occurrence count
🎨Visualization
Statistics Matrix Table: A 9-column by 8-row grid with RSI states labeling vertical axis and indicator combinations on horizontal axis, using compact abbreviations (XOverS, OverB, MACD↑, Vol↓, P↑) for space efficiency
Active Cell Indicator: The current market state cell displays “⦿ NOW ⦿” in yellow text with enhanced color saturation to immediately draw attention to relevant historical performance
Signal Strength Visualization: Info panel uses emoji indicators (🔥 Strong Bullish, ✅ Bullish, ↗️ Weak Bullish, ➖ Neutral, ↘️ Weak Bearish, ⛔ Bearish, ❄️ Strong Bearish, ⚠️ Insufficient Data) for rapid interpretation
Histogram Plot: Below the price chart, a green/red histogram displays the current cell’s average return percentage, providing a time-series view of how historical performance changes as market conditions evolve
Color Intensity Scaling: Cell background transparency and saturation dynamically adjust based on both the magnitude of average returns and the occurrence count, ensuring visual emphasis on reliable patterns
Confidence Level Display: Info panel bottom row shows “High Confidence” (green), “Medium Confidence” (orange), or “Low Confidence” (red) based on occurrence counts relative to minimum threshold multipliers
📖Usage Guidelines
RSI Period
Default: 14
Range: 1 to unlimited
Description: Controls the lookback period for RSI momentum calculation. Standard 14-period provides widely-recognized overbought/oversold levels. Decrease for faster, more sensitive RSI reactions suitable for scalping. Increase (21, 28) for smoother, longer-term momentum assessment in swing trading. Changes affect how quickly the indicator moves between the 7 RSI state classifications.
MACD Fast Length
Default: 12
Range: 1 to unlimited
Description: Sets the faster exponential moving average for MACD calculation. Standard 12-period setting works well for daily charts and captures short-term momentum shifts. Decreasing creates more responsive MACD crossovers but increases false signals. Increasing smooths out noise but delays signal generation, affecting the bullish/bearish indicator state classification.
MACD Slow Length
Default: 26
Range: 1 to unlimited
Description: Defines the slower exponential moving average for MACD calculation. Traditional 26-period setting balances trend identification with responsiveness. Must be greater than Fast Length. Wider spread between fast and slow increases MACD sensitivity to trend changes, impacting the frequency of indicator state transitions in the matrix.
MACD Signal Length
Default: 9
Range: 1 to unlimited
Description: Smoothing period for the MACD signal line that triggers bullish/bearish state changes. Standard 9-period provides reliable crossover signals. Shorter values create more frequent state changes and earlier signals but with more whipsaws. Longer values produce more confirmed, stable signals but with increased lag in detecting momentum shifts.
Volume MA Period
Default: 20
Range: 1 to unlimited
Description: Lookback period for volume moving average used to classify volume as “high” or “low” in indicator state combinations. 20-period default captures typical monthly trading patterns. Shorter periods (10-15) make volume classification more reactive to recent spikes. Longer periods (30-50) require more sustained volume changes to trigger state classification shifts.
Statistics Lookback Period
Default: 200
Range: 50 to 500
Description: Number of historical bars used to calculate matrix statistics. 200 bars provides substantial data for reliable patterns while remaining responsive to regime changes. Lower values (50-100) emphasize recent market behavior and adapt quickly but may produce volatile statistics. Higher values (300-500) capture long-term patterns with stable statistics but slower adaptation to changing market dynamics.
Forward Performance Bars
Default: 5
Range: 1 to 20
Description: Number of bars ahead used to calculate forward returns from each historical state occurrence. 5-bar default suits intraday to short-term swing trading (5 hours on hourly charts, 1 week on daily charts). Lower values (1-3) target short-term momentum trades. Higher values (10-20) align with position trading and longer-term pattern exploitation.
Color Intensity Sensitivity
Default: 2.0
Range: 0.5 to 5.0, step 0.5
Description: Amplifies or dampens the color intensity response to average return magnitudes in the matrix heat map. 2.0 default provides balanced visual emphasis. Lower values (0.5-1.0) create subtle coloring requiring larger returns for full saturation, useful for volatile instruments. Higher values (3.0-5.0) produce vivid colors from smaller returns, highlighting subtle edges in range-bound markets.
Minimum Occurrences for Coloring
Default: 3
Range: 1 to 10
Description: Required minimum sample size before applying color-coded performance to matrix cells. Cells with fewer occurrences display gray “insufficient data” warning. 3-occurrence default filters out rare patterns. Lower threshold (1-2) shows more data but includes unreliable single-event statistics. Higher thresholds (5-10) ensure only well-established patterns receive visual emphasis.
Table Position
Default: top_right
Options: top_left, top_right, bottom_left, bottom_right
Description: Screen location for the 56-cell statistics matrix table. Position to avoid overlapping critical price action or other indicators on your chart. Consider chart orientation and candlestick density when selecting optimal placement.
Show Current State Panel
Default: true
Options: true, false
Description: Toggle visibility of the dedicated current state information panel. When enabled, displays signal strength, RSI value, indicator status, average return, estimated win rate, and confidence level for active market conditions. Disable to declutter charts when only the matrix table is needed.
Info Panel Position
Default: bottom_left
Options: top_left, top_right, bottom_left, bottom_right
Description: Screen location for the current state information panel (when enabled). Position independently from statistics matrix to optimize chart real estate. Typically placed opposite the matrix table for balanced visual layout.
Win Rate Smoothing Strength
Default: 5
Range: 1 to 20
Description: Controls Bayesian prior weighting for estimated win rate calculations. Acts as virtual sample size assuming 50% win rate baseline. Default 5 provides moderate smoothing preventing extreme win rate estimates from small samples. Lower values (1-3) reduce smoothing effect, allowing win rates to reflect raw data more directly. Higher values (10-20) increase conservatism, pulling win rate estimates toward 50% until substantial evidence accumulates.
✅Best Use Cases
Pattern-based discretionary trading where you want historical confirmation before entering setups that “look good” based on current technical alignment
Swing trading with holding periods matching your forward performance bar setting, using high-confidence bullish cells as entry filters
Risk assessment and position sizing, allocating larger size to trades originating from cells with strong positive average returns and high estimated win rates
Market regime identification by observing which RSI states and indicator combinations are currently producing the most reliable historical patterns
Backtesting validation by comparing your manual strategy signals against the historical performance of the corresponding matrix cells
Educational tool for developing intuition about which technical condition combinations have actually worked versus those that feel right but lack historical evidence
⚠️Limitations
Historical patterns do not guarantee future performance, especially during unprecedented market events or regime changes not represented in the lookback period
Small sample sizes (low occurrence counts) produce unreliable statistics despite Bayesian smoothing, requiring caution when acting on low-confidence cells
Matrix statistics lag behind rapidly changing market conditions, as the lookback period must accumulate new state occurrences before updating performance data
Forward return calculations use fixed bar periods that may not align with actual trade exit timing, support/resistance levels, or volatility-adjusted profit targets
💡What Makes This Unique
Multi-Dimensional State Space: Unlike single-indicator tools, simultaneously tracks 56 distinct market condition combinations providing granular pattern resolution unavailable in traditional technical analysis
Bayesian Statistical Rigor: Implements proper probabilistic smoothing to prevent overconfidence from limited data, a critical feature missing from most pattern recognition tools
Real-Time Contextual Feedback: The “NOW” marker and dedicated info panel instantly connect current market conditions to their historical performance profile, eliminating guesswork
Transparent Occurrence Counts: Displays sample sizes directly in each cell, allowing traders to judge statistical reliability themselves rather than hiding data quality issues
Fully Customizable Analysis Window: Complete control over lookback depth and forward return horizons lets traders align the tool precisely with their trading timeframe and strategy requirements
🔬How It Works
1. State Classification and Encoding
Each bar’s RSI value is evaluated and assigned to one of 7 discrete states based on threshold levels (0: <20, 1: 20-30, 2: 30-40, 3: 40-60, 4: 60-70, 5: 70-80, 6: >80)
Simultaneously, three binary conditions are evaluated: MACD line position relative to signal line, current volume relative to its moving average, and current close relative to previous close
These three binary conditions are combined into a single indicator state integer (0-7) using binary encoding, creating 8 possible indicator combinations
The RSI state and indicator state are stored together, defining one of 56 possible market condition cells in the matrix
2. Historical Data Accumulation
As each bar completes, the current state classification, closing price, and bar index are stored in rolling arrays maintained at the size specified by the lookback period
When the arrays reach capacity, the oldest data point is removed and the newest added, creating a sliding historical window
This continuous process builds a comprehensive database of past market conditions and their subsequent price movements
3. Forward Return Calculation and Statistics Update
On each bar, the indicator looks back through the stored historical data to find bars where sufficient forward bars exist to measure outcomes
For each historical occurrence, the price change from that bar to the bar N periods ahead (where N is the forward performance bars setting) is calculated as a percentage return
This percentage return is added to the cumulative return total for the specific matrix cell corresponding to that historical bar’s state classification
Occurrence counts are incremented, and wins are tallied for positive returns, building comprehensive statistics for each of the 56 cells
The Bayesian smoothing formula combines these raw statistics with prior assumptions (neutral 50% win rate) weighted by the smoothing strength parameter to produce estimated win rates that remain stable even with small samples
💡Note:
The Historical Matrix Analyzer is designed as a decision support tool, not a standalone trading system. Best results come from using it to validate discretionary trade ideas or filter systematic strategy signals. Always combine matrix insights with proper risk management, position sizing rules, and awareness of broader market context. The estimated win rate feature uses Bayesian statistics specifically to prevent false confidence from limited data, but no amount of smoothing can create reliable predictions from fundamentally insufficient sample sizes. Focus on high-confidence cells (green-colored confidence indicators) with occurrence counts well above your minimum threshold for the most actionable insights.
Tzotchev Trend Measure [EdgeTools]Are you still measuring trend strength with moving averages? Here is a better variant at scientific level:
Tzotchev Trend Measure: A Statistical Approach to Trend Following
The Tzotchev Trend Measure represents a sophisticated advancement in quantitative trend analysis, moving beyond traditional moving average-based indicators toward a statistically rigorous framework for measuring trend strength. This indicator implements the methodology developed by Tzotchev et al. (2015) in their seminal J.P. Morgan research paper "Designing robust trend-following system: Behind the scenes of trend-following," which introduced a probabilistic approach to trend measurement that has since become a cornerstone of institutional trading strategies.
Mathematical Foundation and Statistical Theory
The core innovation of the Tzotchev Trend Measure lies in its transformation of price momentum into a probability-based metric through the application of statistical hypothesis testing principles. The indicator employs the fundamental formula ST = 2 × Φ(√T × r̄T / σ̂T) - 1, where ST represents the trend strength score bounded between -1 and +1, Φ(x) denotes the normal cumulative distribution function, T represents the lookback period in trading days, r̄T is the average logarithmic return over the specified period, and σ̂T represents the estimated daily return volatility.
This formulation transforms what is essentially a t-statistic into a probabilistic trend measure, testing the null hypothesis that the mean return equals zero against the alternative hypothesis of non-zero mean return. The use of logarithmic returns rather than simple returns provides several statistical advantages, including symmetry properties where log(P₁/P₀) = -log(P₀/P₁), additivity characteristics that allow for proper compounding analysis, and improved validity of normal distribution assumptions that underpin the statistical framework.
The implementation utilizes the Abramowitz and Stegun (1964) approximation for the normal cumulative distribution function, achieving accuracy within ±1.5 × 10⁻⁷ for all input values. This approximation employs Horner's method for polynomial evaluation to ensure numerical stability, particularly important when processing large datasets or extreme market conditions.
Comparative Analysis with Traditional Trend Measurement Methods
The Tzotchev Trend Measure demonstrates significant theoretical and empirical advantages over conventional trend analysis techniques. Traditional moving average-based systems, including simple moving averages (SMA), exponential moving averages (EMA), and their derivatives such as MACD, suffer from several fundamental limitations that the Tzotchev methodology addresses systematically.
Moving average systems exhibit inherent lag bias, as documented by Kaufman (2013) in "Trading Systems and Methods," where he demonstrates that moving averages inevitably lag price movements by approximately half their period length. This lag creates delayed signal generation that reduces profitability in trending markets and increases false signal frequency during consolidation periods. In contrast, the Tzotchev measure eliminates lag bias by directly analyzing the statistical properties of return distributions rather than smoothing price levels.
The volatility normalization inherent in the Tzotchev formula addresses a critical weakness in traditional momentum indicators. As shown by Bollinger (2001) in "Bollinger on Bollinger Bands," momentum oscillators like RSI and Stochastic fail to account for changing volatility regimes, leading to inconsistent signal interpretation across different market conditions. The Tzotchev measure's incorporation of return volatility in the denominator ensures that trend strength assessments remain consistent regardless of the underlying volatility environment.
Empirical studies by Hurst, Ooi, and Pedersen (2013) in "Demystifying Managed Futures" demonstrate that traditional trend-following indicators suffer from significant drawdowns during whipsaw markets, with Sharpe ratios frequently below 0.5 during challenging periods. The authors attribute these poor performance characteristics to the binary nature of most trend signals and their inability to quantify signal confidence. The Tzotchev measure addresses this limitation by providing continuous probability-based outputs that allow for more sophisticated risk management and position sizing strategies.
The statistical foundation of the Tzotchev approach provides superior robustness compared to technical indicators that lack theoretical grounding. Fama and French (1988) in "Permanent and Temporary Components of Stock Prices" established that price movements contain both permanent and temporary components, with traditional moving averages unable to distinguish between these elements effectively. The Tzotchev methodology's hypothesis testing framework specifically tests for the presence of permanent trend components while filtering out temporary noise, providing a more theoretically sound approach to trend identification.
Research by Moskowitz, Ooi, and Pedersen (2012) in "Time Series Momentum in the Cross Section of Asset Returns" found that traditional momentum indicators exhibit significant variation in effectiveness across asset classes and time periods. Their study of multiple asset classes over decades revealed that simple price-based momentum measures often fail to capture persistent trends in fixed income and commodity markets. The Tzotchev measure's normalization by volatility and its probabilistic interpretation provide consistent performance across diverse asset classes, as demonstrated in the original J.P. Morgan research.
Comparative performance studies conducted by AQR Capital Management (Asness, Moskowitz, and Pedersen, 2013) in "Value and Momentum Everywhere" show that volatility-adjusted momentum measures significantly outperform traditional price momentum across international equity, bond, commodity, and currency markets. The study documents Sharpe ratio improvements of 0.2 to 0.4 when incorporating volatility normalization, consistent with the theoretical advantages of the Tzotchev approach.
The regime detection capabilities of the Tzotchev measure provide additional advantages over binary trend classification systems. Research by Ang and Bekaert (2002) in "Regime Switches in Interest Rates" demonstrates that financial markets exhibit distinct regime characteristics that traditional indicators fail to capture adequately. The Tzotchev measure's five-tier classification system (Strong Bull, Weak Bull, Neutral, Weak Bear, Strong Bear) provides more nuanced market state identification than simple trend/no-trend binary systems.
Statistical testing by Jegadeesh and Titman (2001) in "Profitability of Momentum Strategies" revealed that traditional momentum indicators suffer from significant parameter instability, with optimal lookback periods varying substantially across market conditions and asset classes. The Tzotchev measure's statistical framework provides more stable parameter selection through its grounding in hypothesis testing theory, reducing the need for frequent parameter optimization that can lead to overfitting.
Advanced Noise Filtering and Market Regime Detection
A significant enhancement over the original Tzotchev methodology is the incorporation of a multi-factor noise filtering system designed to reduce false signals during sideways market conditions. The filtering mechanism employs four distinct approaches: adaptive thresholding based on current market regime strength, volatility-based filtering utilizing ATR percentile analysis, trend strength confirmation through momentum alignment, and a comprehensive multi-factor approach that combines all methodologies.
The adaptive filtering system analyzes market microstructure through price change relative to average true range, calculates volatility percentiles over rolling windows, and assesses trend alignment across multiple timeframes using exponential moving averages of varying periods. This approach addresses one of the primary limitations identified in traditional trend-following systems, namely their tendency to generate excessive false signals during periods of low volatility or sideways price action.
The regime detection component classifies market conditions into five distinct categories: Strong Bull (ST > 0.3), Weak Bull (0.1 < ST ≤ 0.3), Neutral (-0.1 ≤ ST ≤ 0.1), Weak Bear (-0.3 ≤ ST < -0.1), and Strong Bear (ST < -0.3). This classification system provides traders with clear, quantitative definitions of market regimes that can inform position sizing, risk management, and strategy selection decisions.
Professional Implementation and Trading Applications
The indicator incorporates three distinct trading profiles designed to accommodate different investment approaches and risk tolerances. The Conservative profile employs longer lookback periods (63 days), higher signal thresholds (0.2), and reduced filter sensitivity (0.5) to minimize false signals and focus on major trend changes. The Balanced profile utilizes standard academic parameters with moderate settings across all dimensions. The Aggressive profile implements shorter lookback periods (14 days), lower signal thresholds (-0.1), and increased filter sensitivity (1.5) to capture shorter-term trend movements.
Signal generation occurs through threshold crossover analysis, where long signals are generated when the trend measure crosses above the specified threshold and short signals when it crosses below. The implementation includes sophisticated signal confirmation mechanisms that consider trend alignment across multiple timeframes and momentum strength percentiles to reduce the likelihood of false breakouts.
The alert system provides real-time notifications for trend threshold crossovers, strong regime changes, and signal generation events, with configurable frequency controls to prevent notification spam. Alert messages are standardized to ensure consistency across different market conditions and timeframes.
Performance Optimization and Computational Efficiency
The implementation incorporates several performance optimization features designed to handle large datasets efficiently. The maximum bars back parameter allows users to control historical calculation depth, with default settings optimized for most trading applications while providing flexibility for extended historical analysis. The system includes automatic performance monitoring that generates warnings when computational limits are approached.
Error handling mechanisms protect against division by zero conditions, infinite values, and other numerical instabilities that can occur during extreme market conditions. The finite value checking system ensures data integrity throughout the calculation process, with fallback mechanisms that maintain indicator functionality even when encountering corrupted or missing price data.
Timeframe validation provides warnings when the indicator is applied to unsuitable timeframes, as the Tzotchev methodology was specifically designed for daily and higher timeframe analysis. This validation helps prevent misapplication of the indicator in contexts where its statistical assumptions may not hold.
Visual Design and User Interface
The indicator features eight professional color schemes designed for different trading environments and user preferences. The EdgeTools theme provides an institutional blue and steel color palette suitable for professional trading environments. The Gold theme offers warm colors optimized for commodities trading. The Behavioral theme incorporates psychology-based color contrasts that align with behavioral finance principles. The Quant theme provides neutral colors suitable for analytical applications.
Additional specialized themes include Ocean, Fire, Matrix, and Arctic variations, each optimized for specific visual preferences and trading contexts. All color schemes include automatic dark and light mode optimization to ensure optimal readability across different chart backgrounds and trading platforms.
The information table provides real-time display of key metrics including current trend measure value, market regime classification, signal strength, Z-score, average returns, volatility measures, filter threshold levels, and filter effectiveness percentages. This comprehensive dashboard allows traders to monitor all relevant indicator components simultaneously.
Theoretical Implications and Research Context
The Tzotchev Trend Measure addresses several theoretical limitations inherent in traditional technical analysis approaches. Unlike moving average-based systems that rely on price level comparisons, this methodology grounds trend analysis in statistical hypothesis testing, providing a more robust theoretical foundation for trading decisions.
The probabilistic interpretation of trend strength offers significant advantages over binary trend classification systems. Rather than simply indicating whether a trend exists, the measure quantifies the statistical confidence level associated with the trend assessment, allowing for more nuanced risk management and position sizing decisions.
The incorporation of volatility normalization addresses the well-documented problem of volatility clustering in financial time series, ensuring that trend strength assessments remain consistent across different market volatility regimes. This normalization is particularly important for portfolio management applications where consistent risk metrics across different assets and time periods are essential.
Practical Applications and Trading Strategy Integration
The Tzotchev Trend Measure can be effectively integrated into various trading strategies and portfolio management frameworks. For trend-following strategies, the indicator provides clear entry and exit signals with quantified confidence levels. For mean reversion strategies, extreme readings can signal potential turning points. For portfolio allocation, the regime classification system can inform dynamic asset allocation decisions.
The indicator's statistical foundation makes it particularly suitable for quantitative trading strategies where systematic, rules-based approaches are preferred over discretionary decision-making. The standardized output range facilitates easy integration with position sizing algorithms and risk management systems.
Risk management applications benefit from the indicator's ability to quantify trend strength and provide early warning signals of potential trend changes. The multi-timeframe analysis capability allows for the construction of robust risk management frameworks that consider both short-term tactical and long-term strategic market conditions.
Implementation Guide and Parameter Configuration
The practical application of the Tzotchev Trend Measure requires careful parameter configuration to optimize performance for specific trading objectives and market conditions. This section provides comprehensive guidance for parameter selection and indicator customization.
Core Calculation Parameters
The Lookback Period parameter controls the statistical window used for trend calculation and represents the most critical setting for the indicator. Default values range from 14 to 63 trading days, with shorter periods (14-21 days) providing more sensitive trend detection suitable for short-term trading strategies, while longer periods (42-63 days) offer more stable trend identification appropriate for position trading and long-term investment strategies. The parameter directly influences the statistical significance of trend measurements, with longer periods requiring stronger underlying trends to generate significant signals but providing greater reliability in trend identification.
The Price Source parameter determines which price series is used for return calculations. The default close price provides standard trend analysis, while alternative selections such as high-low midpoint ((high + low) / 2) can reduce noise in volatile markets, and volume-weighted average price (VWAP) offers superior trend identification in institutional trading environments where volume concentration matters significantly.
The Signal Threshold parameter establishes the minimum trend strength required for signal generation, with values ranging from -0.5 to 0.5. Conservative threshold settings (0.2 to 0.3) reduce false signals but may miss early trend opportunities, while aggressive settings (-0.1 to 0.1) provide earlier signal generation at the cost of increased false positive rates. The optimal threshold depends on the trader's risk tolerance and the volatility characteristics of the traded instrument.
Trading Profile Configuration
The Trading Profile system provides pre-configured parameter sets optimized for different trading approaches. The Conservative profile employs a 63-day lookback period with a 0.2 signal threshold and 0.5 noise sensitivity, designed for long-term position traders seeking high-probability trend signals with minimal false positives. The Balanced profile uses a 21-day lookback with 0.05 signal threshold and 1.0 noise sensitivity, suitable for swing traders requiring moderate signal frequency with acceptable noise levels. The Aggressive profile implements a 14-day lookback with -0.1 signal threshold and 1.5 noise sensitivity, optimized for day traders and scalpers requiring frequent signal generation despite higher noise levels.
Advanced Noise Filtering System
The noise filtering mechanism addresses the challenge of false signals during sideways market conditions through four distinct methodologies. The Adaptive filter adjusts thresholds based on current trend strength, increasing sensitivity during strong trending periods while raising thresholds during consolidation phases. The Volatility-based filter utilizes Average True Range (ATR) percentile analysis to suppress signals during abnormally volatile conditions that typically generate false trend indications.
The Trend Strength filter requires alignment between multiple momentum indicators before confirming signals, reducing the probability of false breakouts from consolidation patterns. The Multi-factor approach combines all filtering methodologies using weighted scoring to provide the most robust noise reduction while maintaining signal responsiveness during genuine trend initiations.
The Noise Sensitivity parameter controls the aggressiveness of the filtering system, with lower values (0.5-1.0) providing conservative filtering suitable for volatile instruments, while higher values (1.5-2.0) allow more signals through but may increase false positive rates during choppy market conditions.
Visual Customization and Display Options
The Color Scheme parameter offers eight professional visualization options designed for different analytical preferences and market conditions. The EdgeTools scheme provides high contrast visualization optimized for trend strength differentiation, while the Gold scheme offers warm tones suitable for commodity analysis. The Behavioral scheme uses psychological color associations to enhance decision-making speed, and the Quant scheme provides neutral colors appropriate for quantitative analysis environments.
The Ocean, Fire, Matrix, and Arctic schemes offer additional aesthetic options while maintaining analytical functionality. Each scheme includes optimized colors for both light and dark chart backgrounds, ensuring visibility across different trading platform configurations.
The Show Glow Effects parameter enhances plot visibility through multiple layered lines with progressive transparency, particularly useful when analyzing multiple timeframes simultaneously or when working with dense price data that might obscure trend signals.
Performance Optimization Settings
The Maximum Bars Back parameter controls the historical data depth available for calculations, with values ranging from 5,000 to 50,000 bars. Higher values enable analysis of longer-term trend patterns but may impact indicator loading speed on slower systems or when applied to multiple instruments simultaneously. The optimal setting depends on the intended analysis timeframe and available computational resources.
The Calculate on Every Tick parameter determines whether the indicator updates with every price change or only at bar close. Real-time calculation provides immediate signal updates suitable for scalping and day trading strategies, while bar-close calculation reduces computational overhead and eliminates signal flickering during bar formation, preferred for swing trading and position management applications.
Alert System Configuration
The Alert Frequency parameter controls notification generation, with options for all signals, bar close only, or once per bar. High-frequency trading strategies benefit from all signals mode, while position traders typically prefer bar close alerts to avoid premature position entries based on intrabar fluctuations.
The alert system generates four distinct notification types: Long Signal alerts when the trend measure crosses above the positive signal threshold, Short Signal alerts for negative threshold crossings, Bull Regime alerts when entering strong bullish conditions, and Bear Regime alerts for strong bearish regime identification.
Table Display and Information Management
The information table provides real-time statistical metrics including current trend value, regime classification, signal status, and filter effectiveness measurements. The table position can be customized for optimal screen real estate utilization, and individual metrics can be toggled based on analytical requirements.
The Language parameter supports both English and German display options for international users, while maintaining consistent calculation methodology regardless of display language selection.
Risk Management Integration
Effective risk management integration requires coordination between the trend measure signals and position sizing algorithms. Strong trend readings (above 0.5 or below -0.5) support larger position sizes due to higher probability of trend continuation, while neutral readings (between -0.2 and 0.2) suggest reduced position sizes or range-trading strategies.
The regime classification system provides additional risk management context, with Strong Bull and Strong Bear regimes supporting trend-following strategies, while Neutral regimes indicate potential for mean reversion approaches. The filter effectiveness metric helps traders assess current market conditions and adjust strategy parameters accordingly.
Timeframe Considerations and Multi-Timeframe Analysis
The indicator's effectiveness varies across different timeframes, with higher timeframes (daily, weekly) providing more reliable trend identification but slower signal generation, while lower timeframes (hourly, 15-minute) offer faster signals with increased noise levels. Multi-timeframe analysis combining trend alignment across multiple periods significantly improves signal quality and reduces false positive rates.
For optimal results, traders should consider trend alignment between the primary trading timeframe and at least one higher timeframe before entering positions. Divergences between timeframes often signal potential trend reversals or consolidation periods requiring strategy adjustment.
Conclusion
The Tzotchev Trend Measure represents a significant advancement in technical analysis methodology, combining rigorous statistical foundations with practical trading applications. Its implementation of the J.P. Morgan research methodology provides institutional-quality trend analysis capabilities previously available only to sophisticated quantitative trading firms.
The comprehensive parameter configuration options enable customization for diverse trading styles and market conditions, while the advanced noise filtering and regime detection capabilities provide superior signal quality compared to traditional trend-following indicators. Proper parameter selection and understanding of the indicator's statistical foundation are essential for achieving optimal trading results and effective risk management.
References
Abramowitz, M. and Stegun, I.A. (1964). Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. Washington: National Bureau of Standards.
Ang, A. and Bekaert, G. (2002). Regime Switches in Interest Rates. Journal of Business and Economic Statistics, 20(2), 163-182.
Asness, C.S., Moskowitz, T.J., and Pedersen, L.H. (2013). Value and Momentum Everywhere. Journal of Finance, 68(3), 929-985.
Bollinger, J. (2001). Bollinger on Bollinger Bands. New York: McGraw-Hill.
Fama, E.F. and French, K.R. (1988). Permanent and Temporary Components of Stock Prices. Journal of Political Economy, 96(2), 246-273.
Hurst, B., Ooi, Y.H., and Pedersen, L.H. (2013). Demystifying Managed Futures. Journal of Investment Management, 11(3), 42-58.
Jegadeesh, N. and Titman, S. (2001). Profitability of Momentum Strategies: An Evaluation of Alternative Explanations. Journal of Finance, 56(2), 699-720.
Kaufman, P.J. (2013). Trading Systems and Methods. 5th Edition. Hoboken: John Wiley & Sons.
Moskowitz, T.J., Ooi, Y.H., and Pedersen, L.H. (2012). Time Series Momentum. Journal of Financial Economics, 104(2), 228-250.
Tzotchev, D., Lo, A.W., and Hasanhodzic, J. (2015). Designing robust trend-following system: Behind the scenes of trend-following. J.P. Morgan Quantitative Research, Asset Management Division.
Recession Warning Model [BackQuant]Recession Warning Model
Overview
The Recession Warning Model (RWM) is a Pine Script® indicator designed to estimate the probability of an economic recession by integrating multiple macroeconomic, market sentiment, and labor market indicators. It combines over a dozen data series into a transparent, adaptive, and actionable tool for traders, portfolio managers, and researchers. The model provides customizable complexity levels, display modes, and data processing options to accommodate various analytical requirements while ensuring robustness through dynamic weighting and regime-aware adjustments.
Purpose
The RWM fulfills the need for a concise yet comprehensive tool to monitor recession risk. Unlike approaches relying on a single metric, such as yield-curve inversion, or extensive economic reports, it consolidates multiple data sources into a single probability output. The model identifies active indicators, their confidence levels, and the current economic regime, enabling users to anticipate downturns and adjust strategies accordingly.
Core Features
- Indicator Families : Incorporates 13 indicators across five categories: Yield, Labor, Sentiment, Production, and Financial Stress.
- Dynamic Weighting : Adjusts indicator weights based on recent predictive accuracy, constrained within user-defined boundaries.
- Leading and Coincident Split : Separates early-warning (leading) and confirmatory (coincident) signals, with adjustable weighting (default 60/40 mix).
- Economic Regime Sensitivity : Modulates output sensitivity based on market conditions (Expansion, Late-Cycle, Stress, Crisis), using a composite of VIX, yield-curve, financial conditions, and credit spreads.
- Display Options : Supports four modes—Probability (0-100%), Binary (four risk bins), Lead/Coincident, and Ensemble (blended probability).
- Confidence Intervals : Reflects model stability, widening during high volatility or conflicting signals.
- Alerts : Configurable thresholds (Watch, Caution, Warning, Alert) with persistence filters to minimize false signals.
- Data Export : Enables CSV output for probabilities, signals, and regimes, facilitating external analysis in Python or R.
Model Complexity Levels
Users can select from four tiers to balance simplicity and depth:
1. Essential : Focuses on three core indicators—yield-curve spread, jobless claims, and unemployment change—for minimalistic monitoring.
2. Standard : Expands to nine indicators, adding consumer confidence, PMI, VIX, S&P 500 trend, money supply vs. GDP, and the Sahm Rule.
3. Professional : Includes all 13 indicators, incorporating financial conditions, credit spreads, JOLTS vacancies, and wage growth.
4. Research : Unlocks all indicators plus experimental settings for advanced users.
Key Indicators
Below is a summary of the 13 indicators, their data sources, and economic significance:
- Yield-Curve Spread : Difference between 10-year and 3-month Treasury yields. Negative spreads signal banking sector stress.
- Jobless Claims : Four-week moving average of unemployment claims. Sustained increases indicate rising layoffs.
- Unemployment Change : Three-month change in unemployment rate. Sharp rises often precede recessions.
- Sahm Rule : Triggers when unemployment rises 0.5% above its 12-month low, a reliable recession indicator.
- Consumer Confidence : University of Michigan survey. Declines reflect household pessimism, impacting spending.
- PMI : Purchasing Managers’ Index. Values below 50 indicate manufacturing contraction.
- VIX : CBOE Volatility Index. Elevated levels suggest market anticipation of economic distress.
- S&P 500 Growth : Weekly moving average trend. Declines reduce wealth effects, curbing consumption.
- M2 + GDP Trend : Monitors money supply and real GDP. Simultaneous declines signal credit contraction.
- NFCI : Chicago Fed’s National Financial Conditions Index. Positive values indicate tighter conditions.
- Credit Spreads : Proxy for corporate bond spreads using 10-year vs. 2-year Treasury yields. Widening spreads reflect stress.
- JOLTS Vacancies : Job openings data. Significant drops precede hiring slowdowns.
- Wage Growth : Year-over-year change in average hourly earnings. Late-cycle spikes often signal economic overheating.
Data Processing
- Rate of Change (ROC) : Optionally applied to capture momentum in data series (default: 21-bar period).
- Z-Score Normalization : Standardizes indicators to a common scale (default: 252-bar lookback).
- Smoothing : Applies a short moving average to final signals (default: 5-bar period) to reduce noise.
- Binary Signals : Generated for each indicator (e.g., yield-curve inverted or PMI below 50) based on thresholds or Z-score deviations.
Probability Calculation
1. Each indicator’s binary signal is weighted according to user settings or dynamic performance.
2. Weights are normalized to sum to 100% across active indicators.
3. Leading and coincident signals are aggregated separately (if split mode is enabled) and combined using the specified mix.
4. The probability is adjusted by a regime multiplier, amplifying risk during Stress or Crisis regimes.
5. Optional smoothing ensures stable outputs.
Display and Visualization
- Probability Mode : Plots a continuous 0-100% recession probability with color gradients and confidence bands.
- Binary Mode : Categorizes risk into four levels (Minimal, Watch, Caution, Alert) for simplified dashboards.
- Lead/Coincident Mode : Displays leading and coincident probabilities separately to track signal divergence.
- Ensemble Mode : Averages traditional and split probabilities for a balanced view.
- Regime Background : Color-coded overlays (green for Expansion, orange for Late-Cycle, amber for Stress, red for Crisis).
- Analytics Table : Optional dashboard showing probability, confidence, regime, and top indicator statuses.
Practical Applications
- Asset Allocation : Adjust equity or bond exposures based on sustained probability increases.
- Risk Management : Hedge portfolios with VIX futures or options during regime shifts to Stress or Crisis.
- Sector Rotation : Shift toward defensive sectors when coincident signals rise above 50%.
- Trading Filters : Disable short-term strategies during high-risk regimes.
- Event Timing : Scale positions ahead of high-impact data releases when probability and VIX are elevated.
Configuration Guidelines
- Enable ROC and Z-score for consistent indicator comparison unless raw data is preferred.
- Use dynamic weighting with at least one economic cycle of data for optimal performance.
- Monitor stress composite scores above 80 alongside probabilities above 70 for critical risk signals.
- Adjust adaptation speed (default: 0.1) to 0.2 during Crisis regimes for faster indicator prioritization.
- Combine RWM with complementary tools (e.g., liquidity metrics) for intraday or short-term trading.
Limitations
- Macro indicators lag intraday market moves, making RWM better suited for strategic rather than tactical trading.
- Historical data availability may constrain dynamic weighting on shorter timeframes.
- Model accuracy depends on the quality and timeliness of economic data feeds.
Final Note
The Recession Warning Model provides a disciplined framework for monitoring economic downturn risks. By integrating diverse indicators with transparent weighting and regime-aware adjustments, it empowers users to make informed decisions in portfolio management, risk hedging, or macroeconomic research. Regular review of model outputs alongside market-specific tools ensures its effective application across varying market conditions.
Trend Gauge [BullByte]Trend Gauge
Summary
A multi-factor trend detection indicator that aggregates EMA alignment, VWMA momentum scaling, volume spikes, ATR breakout strength, higher-timeframe confirmation, ADX-based regime filtering, and RSI pivot-divergence penalty into one normalized trend score. It also provides a confidence meter, a Δ Score momentum histogram, divergence highlights, and a compact, scalable dashboard for at-a-glance status.
________________________________________
## 1. Purpose of the Indicator
Why this was built
Traders often monitor several indicators in parallel - EMAs, volume signals, volatility breakouts, higher-timeframe trends, ADX readings, divergence alerts, etc., which can be cumbersome and sometimes contradictory. The “Trend Gauge” indicator was created to consolidate these complementary checks into a single, normalized score that reflects the prevailing market bias (bullish, bearish, or neutral) and its strength. By combining multiple inputs with an adaptive regime filter, scaling contributions by magnitude, and penalizing weakening signals (divergence), this tool aims to reduce noise, highlight genuine trend opportunities, and warn when momentum fades.
Key Design Goals
Signal Aggregation
Merged trend-following signals (EMA crossover, ATR breakout, higher-timeframe confirmation) and momentum signals (VWMA thrust, volume spikes) into a unified score that reflects directional bias more holistically.
Market Regime Awareness
Implemented an ADX-style filter to distinguish between trending and ranging markets, reducing the influence of trend signals during sideways phases to avoid false breakouts.
Magnitude-Based Scaling
Replaced binary contributions with scaled inputs: VWMA thrust and ATR breakout are weighted relative to recent averages, allowing for more nuanced score adjustments based on signal strength.
Momentum Divergence Penalty
Integrated pivot-based RSI divergence detection to slightly reduce the overall score when early signs of momentum weakening are detected, improving risk-awareness in entries.
Confidence Transparency
Added a live confidence metric that shows what percentage of enabled sub-indicators currently agree with the overall bias, making the scoring system more interpretable.
Momentum Acceleration Visualization
Plotted the change in score (Δ Score) as a histogram bar-to-bar, highlighting whether momentum is increasing, flattening, or reversing, aiding in more timely decision-making.
Compact Informational Dashboard
Presented a clean, scalable dashboard that displays each component’s status, the final score, confidence %, detected regime (Trending/Ranging), and a labeled strength gauge for quick visual assessment.
________________________________________
## 2. Why a Trader Should Use It
Main benefits and use cases
1. Unified View: Rather than juggling multiple windows or panels, this indicator delivers a single score synthesizing diverse signals.
2. Regime Filtering: In ranging markets, trend signals often generate false entries. The ADX-based regime filter automatically down-weights trend-following components, helping you avoid chasing false breakouts.
3. Nuanced Momentum & Volatility: VWMA and ATR breakout contributions are normalized by recent averages, so strong moves register strongly while smaller fluctuations are de-emphasized.
4. Early Warning of Weakening: Pivot-based RSI divergence is detected and used to slightly reduce the score when price/momentum diverges, giving a cautionary signal before a full reversal.
5. Confidence Meter: See at a glance how many sub-indicators align with the aggregated bias (e.g., “80% confidence” means 4 out of 5 components agree ). This transparency avoids black-box decisions.
6. Trend Acceleration/Deceleration View: The Δ Score histogram visualizes whether the aggregated score is rising (accelerating trend) or falling (momentum fading), supplementing the main oscillator.
7. Compact Dashboard: A corner table lists each check’s status (“Bull”, “Bear”, “Flat” or “Disabled”), plus overall Score, Confidence %, Regime, Trend Strength label, and a gauge bar. Users can scale text size (Normal, Small, Tiny) without removing elements, so the full picture remains visible even in compact layouts.
8. Customizable & Transparent: All components can be enabled/disabled and parameterized (lengths, thresholds, weights). The full Pine code is open and well-commented, letting users inspect or adapt the logic.
9. Alert-ready: Built-in alert conditions fire when the score crosses weak thresholds to bullish/bearish or returns to neutral, enabling timely notifications.
________________________________________
## 3. Component Rationale (“Why These Specific Indicators?”)
Each sub-component was chosen because it adds complementary information about trend or momentum:
1. EMA Cross
o Basic trend measure: compares a faster EMA vs. a slower EMA. Quickly reflects trend shifts but by itself can whipsaw in sideways markets.
2. VWMA Momentum
o Volume-weighted moving average change indicates momentum with volume context. By normalizing (dividing by a recent average absolute change), we capture the strength of momentum relative to recent history. This scaling prevents tiny moves from dominating and highlights genuinely strong momentum.
3. Volume Spikes
o Sudden jumps in volume combined with price movement often accompany stronger moves or reversals. A binary detection (+1 for bullish spike, -1 for bearish spike) flags high-conviction bars.
4. ATR Breakout
o Detects price breaking beyond recent highs/lows by a multiple of ATR. Measures breakout strength by how far beyond the threshold price moves relative to ATR, capped to avoid extreme outliers. This gives a volatility-contextual trend signal.
5. Higher-Timeframe EMA Alignment
o Confirms whether the shorter-term trend aligns with a higher timeframe trend. Uses request.security with lookahead_off to avoid future data. When multiple timeframes agree, confidence in direction increases.
6. ADX Regime Filter (Manual Calculation)
o Computes directional movement (+DM/–DM), smoothes via RMA, computes DI+ and DI–, then a DX and ADX-like value. If ADX ≥ threshold, market is “Trending” and trend components carry full weight; if ADX < threshold, “Ranging” mode applies a configurable weight multiplier (e.g., 0.5) to trend-based contributions, reducing false signals in sideways conditions. Volume spikes remain binary (optional behavior; can be adjusted if desired).
7. RSI Pivot-Divergence Penalty
o Uses ta.pivothigh / ta.pivotlow with a lookback to detect pivot highs/lows on price and corresponding RSI values. When price makes a higher high but RSI makes a lower high (bearish divergence), or price makes a lower low but RSI makes a higher low (bullish divergence), a divergence signal is set. Rather than flipping the trend outright, the indicator subtracts (or adds) a small penalty (configurable) from the aggregated score if it would weaken the current bias. This subtle adjustment warns of weakening momentum without overreacting to noise.
8. Confidence Meter
o Counts how many enabled components currently agree in direction with the aggregated score (i.e., component sign × score sign > 0). Displays this as a percentage. A high percentage indicates strong corroboration; a low percentage warns of mixed signals.
9. Δ Score Momentum View
o Plots the bar-to-bar change in the aggregated score (delta_score = score - score ) as a histogram. When positive, bars are drawn in green above zero; when negative, bars are drawn in red below zero. This reveals acceleration (rising Δ) or deceleration (falling Δ), supplementing the main oscillator.
10. Dashboard
• A table in the indicator pane’s top-right with 11 rows:
1. EMA Cross status
2. VWMA Momentum status
3. Volume Spike status
4. ATR Breakout status
5. Higher-Timeframe Trend status
6. Score (numeric)
7. Confidence %
8. Regime (“Trending” or “Ranging”)
9. Trend Strength label (e.g., “Weak Bullish Trend”, “Strong Bearish Trend”)
10. Gauge bar visually representing score magnitude
• All rows always present; size_opt (Normal, Small, Tiny) only changes text size via text_size, not which elements appear. This ensures full transparency.
________________________________________
## 4. What Makes This Indicator Stand Out
• Regime-Weighted Multi-Factor Score: Trend and momentum signals are adaptively weighted by market regime (trending vs. ranging) , reducing false signals.
• Magnitude Scaling: VWMA and ATR breakout contributions are normalized by recent average momentum or ATR, giving finer gradation compared to simple ±1.
• Integrated Divergence Penalty: Divergence directly adjusts the aggregated score rather than appearing as a separate subplot; this influences alerts and trend labeling in real time.
• Confidence Meter: Shows the percentage of sub-signals in agreement, providing transparency and preventing blind trust in a single metric.
• Δ Score Histogram Momentum View: A histogram highlights acceleration or deceleration of the aggregated trend score, helping detect shifts early.
• Flexible Dashboard: Always-visible component statuses and summary metrics in one place; text size scaling keeps the full picture available in cramped layouts.
• Lookahead-Safe HTF Confirmation: Uses lookahead_off so no future data is accessed from higher timeframes, avoiding repaint bias.
• Repaint Transparency: Divergence detection uses pivot functions that inherently confirm only after lookback bars; description documents this lag so users understand how and when divergence labels appear.
• Open-Source & Educational: Full, well-commented Pine v6 code is provided; users can learn from its structure: manual ADX computation, conditional plotting with series = show ? value : na, efficient use of table.new in barstate.islast, and grouped inputs with tooltips.
• Compliance-Conscious: All plots have descriptive titles; inputs use clear names; no unnamed generic “Plot” entries; manual ADX uses RMA; all request.security calls use lookahead_off. Code comments mention repaint behavior and limitations.
________________________________________
## 5. Recommended Timeframes & Tuning
• Any Timeframe: The indicator works on small (e.g., 1m) to large (daily, weekly) timeframes. However:
o On very low timeframes (<1m or tick charts), noise may produce frequent whipsaws. Consider increasing smoothing lengths, disabling certain components (e.g., volume spike if volume data noisy), or using a larger pivot lookback for divergence.
o On higher timeframes (daily, weekly), consider longer lookbacks for ATR breakout or divergence, and set Higher-Timeframe trend appropriately (e.g., 4H HTF when on 5 Min chart).
• Defaults & Experimentation: Default input values are chosen to be balanced for many liquid markets. Users should test with replay or historical analysis on their symbol/timeframe and adjust:
o ADX threshold (e.g., 20–30) based on instrument volatility.
o VWMA and ATR scaling lengths to match average volatility cycles.
o Pivot lookback for divergence: shorter for faster markets, longer for slower ones.
• Combining with Other Analysis: Use in conjunction with price action, support/resistance, candlestick patterns, order flow, or other tools as desired. The aggregated score and alerts can guide attention but should not be the sole decision-factor.
________________________________________
## 6. How Scoring and Logic Works (Step-by-Step)
1. Compute Sub-Scores
o EMA Cross: Evaluate fast EMA > slow EMA ? +1 : fast EMA < slow EMA ? -1 : 0.
o VWMA Momentum: Calculate vwma = ta.vwma(close, length), then vwma_mom = vwma - vwma . Normalize: divide by recent average absolute momentum (e.g., ta.sma(abs(vwma_mom), lookback)), clip to .
o Volume Spike: Compute vol_SMA = ta.sma(volume, len). If volume > vol_SMA * multiplier AND price moved up ≥ threshold%, assign +1; if moved down ≥ threshold%, assign -1; else 0.
o ATR Breakout: Determine recent high/low over lookback. If close > high + ATR*mult, compute distance = close - (high + ATR*mult), normalize by ATR, cap at a configured maximum. Assign positive contribution. Similarly for bearish breakout below low.
o Higher-Timeframe Trend: Use request.security(..., lookahead=barmerge.lookahead_off) to fetch HTF EMAs; assign +1 or -1 based on alignment.
2. ADX Regime Weighting
o Compute manual ADX: directional movements (+DM, –DM), smoothed via RMA, DI+ and DI–, then DX and ADX via RMA. If ADX ≥ threshold, market is considered “Trending”; otherwise “Ranging.”
o If trending, trend-based contributions (EMA, VWMA, ATR, HTF) use full weight = 1.0. If ranging, use weight = ranging_weight (e.g., 0.5) to down-weight them. Volume spike stays binary ±1 (optional to change if desired).
3. Aggregate Raw Score
o Sum weighted contributions of all enabled components. Count the number of enabled components; if zero, default count = 1 to avoid division by zero.
4. Divergence Penalty
o Detect pivot highs/lows on price and corresponding RSI values, using a lookback. When price and RSI diverge (bearish or bullish divergence), check if current raw score is in the opposing direction:
If bearish divergence (price higher high, RSI lower high) and raw score currently positive, subtract a penalty (e.g., 0.5).
If bullish divergence (price lower low, RSI higher low) and raw score currently negative, add a penalty.
o This reduces score magnitude to reflect weakening momentum, without flipping the trend outright.
5. Normalize and Smooth
o Normalized score = (raw_score / number_of_enabled_components) * 100. This yields a roughly range.
o Optional EMA smoothing of this normalized score to reduce noise.
6. Interpretation
o Sign: >0 = net bullish bias; <0 = net bearish bias; near zero = neutral.
o Magnitude Zones: Compare |score| to thresholds (Weak, Medium, Strong) to label trend strength (e.g., “Weak Bullish Trend”, “Medium Bearish Trend”, “Strong Bullish Trend”).
o Δ Score Histogram: The histogram bars from zero show change from previous bar’s score; positive bars indicate acceleration, negative bars indicate deceleration.
o Confidence: Percentage of sub-indicators aligned with the score’s sign.
o Regime: Indicates whether trend-based signals are fully weighted or down-weighted.
________________________________________
## 7. Oscillator Plot & Visualization: How to Read It
Main Score Line & Area
The oscillator plots the aggregated score as a line, with colored fill: green above zero for bullish area, red below zero for bearish area. Horizontal reference lines at ±Weak, ±Medium, and ±Strong thresholds mark zones: crossing above +Weak suggests beginning of bullish bias, above +Medium for moderate strength, above +Strong for strong trend; similarly for bearish below negative thresholds.
Δ Score Histogram
If enabled, a histogram shows score - score . When positive, bars appear in green above zero, indicating accelerating bullish momentum; when negative, bars appear in red below zero, indicating decelerating or reversing momentum. The height of each bar reflects the magnitude of change in the aggregated score from the prior bar.
Divergence Highlight Fill
If enabled, when a pivot-based divergence is confirmed:
• Bullish Divergence : fill the area below zero down to –Weak threshold in green, signaling potential reversal from bearish to bullish.
• Bearish Divergence : fill the area above zero up to +Weak threshold in red, signaling potential reversal from bullish to bearish.
These fills appear with a lag equal to pivot lookback (the number of bars needed to confirm the pivot). They do not repaint after confirmation, but users must understand this lag.
Trend Direction Label
When score crosses above or below the Weak threshold, a small label appears near the score line reading “Bullish” or “Bearish.” If the score returns within ±Weak, the label “Neutral” appears. This helps quickly identify shifts at the moment they occur.
Dashboard Panel
In the indicator pane’s top-right, a table shows:
1. EMA Cross status: “Bull”, “Bear”, “Flat”, or “Disabled”
2. VWMA Momentum status: similarly
3. Volume Spike status: “Bull”, “Bear”, “No”, or “Disabled”
4. ATR Breakout status: “Bull”, “Bear”, “No”, or “Disabled”
5. Higher-Timeframe Trend status: “Bull”, “Bear”, “Flat”, or “Disabled”
6. Score: numeric value (rounded)
7. Confidence: e.g., “80%” (colored: green for high, amber for medium, red for low)
8. Regime: “Trending” or “Ranging” (colored accordingly)
9. Trend Strength: textual label based on magnitude (e.g., “Medium Bullish Trend”)
10. Gauge: a bar of blocks representing |score|/100
All rows remain visible at all times; changing Dashboard Size only scales text size (Normal, Small, Tiny).
________________________________________
## 8. Example Usage (Illustrative Scenario)
Example: BTCUSD 5 Min
1. Setup: Add “Trend Gauge ” to your BTCUSD 5 Min chart. Defaults: EMAs (8/21), VWMA 14 with lookback 3, volume spike settings, ATR breakout 14/5, HTF = 5m (or adjust to 4H if preferred), ADX threshold 25, ranging weight 0.5, divergence RSI length 14 pivot lookback 5, penalty 0.5, smoothing length 3, thresholds Weak=20, Medium=50, Strong=80. Dashboard Size = Small.
2. Trend Onset: At some point, price breaks above recent high by ATR multiple, volume spikes upward, faster EMA crosses above slower EMA, HTF EMA also bullish, and ADX (manual) ≥ threshold → aggregated score rises above +20 (Weak threshold) into +Medium zone. Dashboard shows “Bull” for EMA, VWMA, Vol Spike, ATR, HTF; Score ~+60–+70; Confidence ~100%; Regime “Trending”; Trend Strength “Medium Bullish Trend”; Gauge ~6–7 blocks. Δ Score histogram bars are green and rising, indicating accelerating bullish momentum. Trader notes the alignment.
3. Divergence Warning: Later, price makes a slightly higher high but RSI fails to confirm (lower RSI high). Pivot lookback completes; the indicator highlights a bearish divergence fill above zero and subtracts a small penalty from the score, causing score to stall or retrace slightly. Dashboard still bullish but score dips toward +Weak. This warns the trader to tighten stops or take partial profits.
4. Trend Weakens: Score eventually crosses below +Weak back into neutral; a “Neutral” label appears, and a “Neutral Trend” alert fires if enabled. Trader exits or avoids new long entries. If score subsequently crosses below –Weak, a “Bearish” label and alert occur.
5. Customization: If the trader finds VWMA noise too frequent on this instrument, they may disable VWMA or increase lookback. If ATR breakouts are too rare, adjust ATR length or multiplier. If ADX threshold seems off, tune threshold. All these adjustments are explained in Inputs section.
6. Visualization: The screenshot shows the main score oscillator with colored areas, reference lines at ±20/50/80, Δ Score histogram bars below/above zero, divergence fill highlighting potential reversal, and the dashboard table in the top-right.
________________________________________
## 9. Inputs Explanation
A concise yet clear summary of inputs helps users understand and adjust:
1. General Settings
• Theme (Dark/Light): Choose background-appropriate colors for the indicator pane.
• Dashboard Size (Normal/Small/Tiny): Scales text size only; all dashboard elements remain visible.
2. Indicator Settings
• Enable EMA Cross: Toggle on/off basic EMA alignment check.
o Fast EMA Length and Slow EMA Length: Periods for EMAs.
• Enable VWMA Momentum: Toggle VWMA momentum check.
o VWMA Length: Period for VWMA.
o VWMA Momentum Lookback: Bars to compare VWMA to measure momentum.
• Enable Volume Spike: Toggle volume spike detection.
o Volume SMA Length: Period to compute average volume.
o Volume Spike Multiplier: How many times above average volume qualifies as spike.
o Min Price Move (%): Minimum percent change in price during spike to qualify as bullish or bearish.
• Enable ATR Breakout: Toggle ATR breakout detection.
o ATR Length: Period for ATR.
o Breakout Lookback: Bars to look back for recent highs/lows.
o ATR Multiplier: Multiplier for breakout threshold.
• Enable Higher Timeframe Trend: Toggle HTF EMA alignment.
o Higher Timeframe: E.g., “5” for 5-minute when on 1-minute chart, or “60” for 5 Min when on 15m, etc. Uses lookahead_off.
• Enable ADX Regime Filter: Toggles regime-based weighting.
o ADX Length: Period for manual ADX calculation.
o ADX Threshold: Value above which market considered trending.
o Ranging Weight Multiplier: Weight applied to trend components when ADX < threshold (e.g., 0.5).
• Scale VWMA Momentum: Toggle normalization of VWMA momentum magnitude.
o VWMA Mom Scale Lookback: Period for average absolute VWMA momentum.
• Scale ATR Breakout Strength: Toggle normalization of breakout distance by ATR.
o ATR Scale Cap: Maximum multiple of ATR used for breakout strength.
• Enable Price-RSI Divergence: Toggle divergence detection.
o RSI Length for Divergence: Period for RSI.
o Pivot Lookback for Divergence: Bars on each side to identify pivot high/low.
o Divergence Penalty: Amount to subtract/add to score when divergence detected (e.g., 0.5).
3. Score Settings
• Smooth Score: Toggle EMA smoothing of normalized score.
• Score Smoothing Length: Period for smoothing EMA.
• Weak Threshold: Absolute score value under which trend is considered weak or neutral.
• Medium Threshold: Score above Weak but below Medium is moderate.
• Strong Threshold: Score above this indicates strong trend.
4. Visualization Settings
• Show Δ Score Histogram: Toggle display of the bar-to-bar change in score as a histogram. Default true.
• Show Divergence Fill: Toggle background fill highlighting confirmed divergences. Default true.
Each input has a tooltip in the code.
________________________________________
## 10. Limitations, Repaint Notes, and Disclaimers
10.1. Repaint & Lag Considerations
• Pivot-Based Divergence Lag: The divergence detection uses ta.pivothigh / ta.pivotlow with a specified lookback. By design, a pivot is only confirmed after the lookback number of bars. As a result:
o Divergence labels or fills appear with a delay equal to the pivot lookback.
o Once the pivot is confirmed and the divergence is detected, the fill/label does not repaint thereafter, but you must understand and accept this lag.
o Users should not treat divergence highlights as predictive signals without additional confirmation, because they appear after the pivot has fully formed.
• Higher-Timeframe EMA Alignment: Uses request.security(..., lookahead=barmerge.lookahead_off), so no future data from the higher timeframe is used. This avoids lookahead bias and ensures signals are based only on completed higher-timeframe bars.
• No Future Data: All calculations are designed to avoid using future information. For example, manual ADX uses RMA on past data; security calls use lookahead_off.
10.2. Market & Noise Considerations
• In very choppy or low-liquidity markets, some components (e.g., volume spikes or VWMA momentum) may be noisy. Users can disable or adjust those components’ parameters.
• On extremely low timeframes, noise may dominate; consider smoothing lengths or disabling certain features.
• On very high timeframes, pivots and breakouts occur less frequently; adjust lookbacks accordingly to avoid sparse signals.
10.3. Not a Standalone Trading System
• This is an indicator, not a complete trading strategy. It provides signals and context but does not manage entries, exits, position sizing, or risk management.
• Users must combine it with their own analysis, money management, and confirmations (e.g., price patterns, support/resistance, fundamental context).
• No guarantees: past behavior does not guarantee future performance.
10.4. Disclaimers
• Educational Purposes Only: The script is provided as-is for educational and informational purposes. It does not constitute financial, investment, or trading advice.
• Use at Your Own Risk: Trading involves risk of loss. Users should thoroughly test and use proper risk management.
• No Guarantees: The author is not responsible for trading outcomes based on this indicator.
• License: Published under Mozilla Public License 2.0; code is open for viewing and modification under MPL terms.
________________________________________
## 11. Alerts
• The indicator defines three alert conditions:
1. Bullish Trend: when the aggregated score crosses above the Weak threshold.
2. Bearish Trend: when the score crosses below the negative Weak threshold.
3. Neutral Trend: when the score returns within ±Weak after being outside.
Good luck
– BullByte
TUF_LOGICThe TUF_LOGIC library incorporates three-valued logic (also known as trilean logic) into Pine Script, enabling the representation of states beyond the binary True and False to include an 'Uncertain' state. This addition is particularly apt for financial market contexts where information may not always be black or white, accommodating scenarios of partial or ambiguous data.
Key Features:
Trilean Data Type: Defines a tri type, facilitating the representation of True (1), Uncertain (0), and False (-1) states, thus accommodating a more nuanced approach to logical evaluation.
Validation and Conversion: Includes methods like validate, to ensure trilean variables conform to expected states, and to_bool, for converting trilean to boolean values, enhancing interoperability with binary logic systems.
Core Logical Operations: Extends traditional logical operators (AND, OR, NOT, XOR, EQUALITY) to work within the trilean domain, enabling complex conditionals that reflect real-world uncertainties.
Specialized Logical Operations:
Implication Operators: Features IMP_K (Kleene's), IMP_L (Łukasiewicz's), and IMP_RM3, offering varied approaches to logical implication within the trilean framework.
Possibility, Necessity, and Contingency Operators: Implements MA ("it is possible that..."), LA ("it is necessary that..."), and IA ("it is unknown/contingent that..."), derived from Tarski-Łukasiewicz's modal logic attempts, enriching the library with modal logic capabilities.
Unanimity Functions: The UNANIMOUS operator assesses complete agreement among trilean values, useful for scenarios requiring consensus or uniformity across multiple indicators or conditions.
This library is developed to support scenarios in financial trading and analysis where decisions might hinge on more than binary outcomes. By incorporating modal logic aspects and providing a framework for handling uncertainty through the MA, LA, and IA operations, TUF_LOGIC bridges the gap between classical binary logic and the realities of uncertain information, making it a valuable tool for developing sophisticated trading strategies and analytical models.
Library "TUF_LOGIC"
3VL Implementation (TUF stands for True, Uncertain, False.)
method validate(self)
Ensures a valid trilean variable. This works by clamping the variable to the range associated with the trilean type.
Namespace types: tri
Parameters:
self (tri)
Returns: Validated trilean object.
method to_bool(self)
Converts a trilean object into a boolean object. True -> True, Uncertain -> na, False -> False.
Namespace types: tri
Parameters:
self (tri)
Returns: A boolean variable.
method NOT(self)
Negates the trilean object. True -> False, Uncertain -> Uncertain, False -> True
Namespace types: tri
Parameters:
self (tri)
Returns: Negated trilean object.
method AND(self, comparator)
Logical AND operation for trilean objects.
Namespace types: tri
Parameters:
self (tri) : The first trilean object.
comparator (tri) : The second trilean object to compare with.
Returns: `tri` Result of the AND operation as a trilean object.
method OR(self, comparator)
Logical OR operation for trilean objects.
Namespace types: tri
Parameters:
self (tri) : The first trilean object.
comparator (tri) : The second trilean object to compare with.
Returns: `tri` Result of the OR operation as a trilean object.
method EQUALITY(self, comparator)
Logical EQUALITY operation for trilean objects.
Namespace types: tri
Parameters:
self (tri) : The first trilean object.
comparator (tri) : The second trilean object to compare with.
Returns: `tri` Result of the EQUALITY operation as a trilean object, True if both are equal, False otherwise.
method XOR(self, comparator)
Logical XOR (Exclusive OR) operation for trilean objects.
Namespace types: tri
Parameters:
self (tri) : The first trilean object.
comparator (tri) : The second trilean object to compare with.
Returns: `tri` Result of the XOR operation as a trilean object.
method IMP_K(self, comparator)
Material implication using Kleene's logic for trilean objects.
Namespace types: tri
Parameters:
self (tri) : The antecedent trilean object.
comparator (tri) : The consequent trilean object.
Returns: `tri` Result of the implication operation as a trilean object.
method IMP_L(self, comparator)
Logical implication using Łukasiewicz's logic for trilean objects.
Namespace types: tri
Parameters:
self (tri) : The antecedent trilean object.
comparator (tri) : The consequent trilean object.
Returns: `tri` Result of the implication operation as a trilean object.
method IMP_RM3(self, comparator)
Logical implication using RM3 logic for trilean objects.
Namespace types: tri
Parameters:
self (tri) : The antecedent trilean object.
comparator (tri) : The consequent trilean object.
Returns: `tri` Result of the RM3 implication as a trilean object.
method MA(self)
Evaluates to True if the trilean object is either True or Uncertain, False otherwise.
Namespace types: tri
Parameters:
self (tri) : The trilean object to evaluate.
Returns: `tri` Result of the operation as a trilean object.
method LA(self)
Evaluates to True if the trilean object is True, False otherwise.
Namespace types: tri
Parameters:
self (tri) : The trilean object to evaluate.
Returns: `tri` Result of the operation as a trilean object.
method IA(self)
Evaluates to True if the trilean object is Uncertain, False otherwise.
Namespace types: tri
Parameters:
self (tri) : The trilean object to evaluate.
Returns: `tri` Result of the operation as a trilean object.
UNANIMOUS(self, comparator)
Evaluates the unanimity between two trilean values.
Parameters:
self (tri) : The first trilean value.
comparator (tri) : The second trilean value.
Returns: `tri` Returns True if both values are True, False if both are False, and Uncertain otherwise.
method UNANIMOUS(self)
Evaluates the unanimity among an array of trilean values.
Namespace types: array
Parameters:
self (array) : The array of trilean values.
Returns: `tri` Returns True if all values are True, False if all are False, and Uncertain otherwise.
tri
Three Value Logic (T.U.F.), or trilean. Can be True (1), Uncertain (0), or False (-1).
Fields:
v (series int) : Value of the trilean variable. Can be True (1), Uncertain (0), or False (-1).
SML SuiteIntroducing the "SML Suite" Indicator
The "SML Suite" is a powerful and easy-to-use trading indicator designed to help traders make informed decisions in the world of financial markets. Whether you're a seasoned trader or a novice, this indicator is your trusty sidekick for evaluating market trends.
Key Features:
Three Moving Averages: The indicator employs three different moving averages, each with a distinct length, allowing you to adapt to various market conditions.
Customizable Parameters: You can easily customize the moving average lengths and source data to tailor the indicator to your specific trading strategy.
Standard Deviation Multiplier: Adjust the standard deviation multiplier to fine-tune the indicator's sensitivity to market fluctuations.
Binary Results: The indicator provides clear binary signals (1 or -1) based on whether the current price is above or below certain bands. This simplifies your decision-making process.
SML Calculation: The SML (Short, Medium, Long) calculation is a smart combination of the binary results, offering you an overall sentiment about the market.
Color-Coded Visualization: Visualize market sentiment with color-coded bars, making it easy to spot trends at a glance.
Interactive Table: A table is displayed on your chart, giving you a quick overview of the binary results and the overall SML sentiment.
With the "SML Suite" indicator, you don't need to be a coding expert to harness the power of technical analysis. Stay ahead of the game and enhance your trading strategy with this user-friendly tool. Make your trading decisions with confidence and clarity, backed by the insights provided by the "SML Suite" indicator.
fuson DEMA-->it does not need to be played with any settings. so I did not add a period.
-->l shows bearish trends very well but not as good as bearish trends in bullish trends
-->vdub can be used with binary options v3 and increases the leakage rates very high
-->If used for forex, it can be used in periods of 1 hour and longer
-->vdub binary option v3can be used for 1 minute verification with binary option if it will be used in binary option
QTechLabs Machine Learning Logistic Regression Indicator [Lite]QTechLabs Machine Learning Logistic Regression Indicator
Ver5.1 1st January 2026
Author: QTechLabs
Description
A lightweight logistic-regression-based signal indicator (Q# ML Logistic Regression Indicator ) for TradingView. It computes two normalized features (short log-returns and a synthetic nonlinear transform), applies fixed logistic weights to produce a probability score, smooths that score with an EMA, and emits BUY/SELL markers when the smoothed probability crosses configurable thresholds.
Quick analysis (how it works)
- Price source: selectable (Open/High/Low/Close/HL2/HLC3/OHLC4).
- Features:
- ret = log(ds / ds ) — short log-return over ret_lookback bars.
- synthetic = log(abs(ds^2 - 1) + 0.5) — a nonlinear “synthetic” feature.
- Both features normalized over a 20‑bar window to range ~0–1.
- Fixed logistic regression weights: w0 = -2.0 (bias), w1 = 2.0 (ret), w2 = 1.0 (synthetic).
- Probability = sigmoid(w0 + w1*norm_ret + w2*norm_synthetic).
- Smoothed probability = EMA(prob, smooth_len).
- Signals:
- BUY when sprob > threshold.
- SELL when sprob < (1 - threshold).
- Visual buy/sell shapes plotted and alert conditions provided.
- Defaults: threshold = 0.6, ret_lookback = 3, smooth_len = 3.
User instructions
1. Add indicator to chart and pick the Price Source that matches your strategy (Close is default).
2. Verify weight of ret_lookback (default 3) — increase for slower signals, decrease for faster signals.
3. Threshold: default 0.6 — higher = fewer signals (more confidence), lower = more signals. Recommended range 0.55–0.75.
4. Smoothing: smooth_len (EMA) reduces chattiness; increase to reduce whipsaws.
5. Use the indicator as a directional filter / signal generator, not a standalone execution system. Combine with trend confirmation (e.g., higher-timeframe MA) and risk management.
6. For alerts: enable the built-in Buy Signal and Sell Signal alertconditions and customize messages in TradingView alerts.
7. Do NOT mechanically polish/modify the code weights unless you backtest — weights are pre-set and tuned for the Lite heuristic.
Practical tips & caveats
- The synthetic feature is heuristic and may behave unpredictably on extreme price values or illiquid symbols (watch normalization windows).
- Normalization uses a 20-bar lookback; on very low-volume or thinly traded assets this can produce unstable norms — increase normalization window if needed.
- This is a simple model: expect false signals in choppy ranges. Always backtest on your instrument and timeframe.
- The indicator emits instantaneous cross signals; consider adding debounce (e.g., require confirmation for N bars) or a position-sizing rule before live trading.
- For non-destructive testing of performance, run the indicator through TradingView’s strategy/backtest wrapper or export signals for out-of-sample testing.
Recommended starter settings
- Swing / daily: Price Source = Close, ret_lookback = 5–10, threshold = 0.62–0.68, smooth_len = 5–10.
- Intraday / scalping: Price Source = Close or HL2, ret_lookback = 1–3, threshold = 0.55–0.62, smooth_len = 2–4.
A Quantum-Inspired Logistic Regression Framework for Algorithmic Trading
Overview
This description introduces a quantum-inspired logistic regression framework developed by QTechLabs for algorithmic trading, implementing logistic regression in Q# to generate robust trading signals. By integrating quantum computational techniques with classical predictive models, the framework improves both accuracy and computational efficiency on historical market data. Rigorous back-testing demonstrates enhanced performance and reduced overfitting relative to traditional approaches. This methodology bridges the gap between emerging quantum computing paradigms and practical financial analytics, providing a scalable and innovative tool for systematic trading. Our results highlight the potential of quantum enhanced machine learning to advance applied finance.
Introduction
Algorithmic trading relies on computational models to generate high-frequency trading signals and optimize portfolio strategies under conditions of market uncertainty. Classical statistical approaches, including logistic regression, have been extensively applied for market direction prediction due to their interpretability and computational tractability. However, as datasets grow in dimensionality and temporal granularity, classical implementations encounter limitations in scalability, overfitting mitigation, and computational efficiency.
Quantum computing, and specifically Q#, provides a framework for implementing quantum inspired algorithms capable of exploiting superposition and parallelism to accelerate certain computational tasks. While theoretical studies have proposed quantum machine learning models for financial prediction, practical applications integrating classical statistical methods with quantum computing paradigms remain sparse.
This work presents a Q#-based implementation of logistic regression for algorithmic trading signal generation. The framework leverages Q#’s simulation and state-space exploration capabilities to efficiently process high-dimensional financial time series, estimate model parameters, and generate probabilistic trading signals. Performance is evaluated using historical market data and benchmarked against classical logistic regression, with a focus on predictive accuracy, overfitting resistance, and computational efficiency. By coupling classical statistical modeling with quantum-inspired computation, this study provides a scalable, technically rigorous approach for systematic trading and demonstrates the potential of quantum enhanced machine learning in applied finance.
Methodology
1. Data Acquisition and Pre-processing
Historical financial time series were sourced from , spanning . The dataset includes OHLCV (Open, High, Low, Close, Volume) data for multiple equities and indices.
Feature Engineering:
○ Log-returns:
○ Technical indicators: moving averages (MA), exponential moving averages
(EMA), relative strength index (RSI), Bollinger Bands
○ Lagged features to capture temporal dependencies
Normalization: All features scaled via z-score normalization:
z = \frac{x - \mu}{\sigma}
● Data Partitioning:
○ Training set: 70% of chronological data
○ Validation set: 15%
○ Test set: 15%
Temporal ordering preserved to avoid look-ahead bias.
Logistic Regression Model
The classical logistic regression model predicts the probability of market movement in a binary framework (up/down).
Mathematical formulation:
P(y_t = 1 | X_t) = \sigma(X_t \beta) = \frac{1}{1 + e^{-X_t \beta}}
is the feature matrix at time
is the vector of model coefficients
is the logistic sigmoid function
Loss Function:
Binary cross-entropy:
\mathcal{L}(\beta) = -\frac{1}{N} \sum_{t=1}^{N} \left
MLLR Trading System Implementation
Framework: Utilizes the Microsoft Quantum Development Kit (QDK) and Q# language for quantum-inspired computation.
Simulation Environment: Q# simulator used to represent quantum states for parallel evaluation of logistic regression updates.
Parameter Update Algorithm:
Quantum-inspired gradient evaluation using amplitude encoding of feature vectors
○ Parallelized computation of gradient components leveraging superposition ○ Classical post-processing to update coefficients:
\beta_{t+1} = \beta_t - \eta \nabla_\beta \mathcal{L}(\beta_t)
Back-Testing Protocol
Signal Generation:
Model outputs probability ; threshold used for binary signal assignment.
○ Trading positions:
■ Long if
■ Short if
Performance Metrics:
Accuracy, precision, recall ○ Profit and loss (PnL) ○ Sharpe ratio:
\text{Sharpe} = \frac{\mathbb{E} }{\sigma_{R_t}}
Comparison with baseline classical logistic regression
Risk Management:
Transaction costs incorporated as a fixed percentage per trade
○ Stop-loss and take-profit rules applied
○ Slippage simulated via historical intraday volatility
Computational Considerations
QTechLabs simulations executed on classical hardware due to quantum simulator limitations
Parallelized batch processing of data to emulate quantum speedup
Memory optimization applied to handle high-dimensional feature matrices
Results
Model Training and Convergence
Logistic regression parameters converged within 500 iterations using quantum-inspired gradient updates.
Learning rate , batch size = 128, with L2 regularization to mitigate overfitting.
Convergence criteria: change in loss over 10 consecutive iterations.
Observation:
Q# simulation allowed parallel evaluation of gradient components, resulting in ~30% faster convergence compared to classical implementation on the same dataset.
Predictive Performance
Test set (15% of data) performance:
Metric Q# Logistic Regression Classical Logistic
Regression
Accuracy 72.4% 68.1%
Precision 70.8% 66.2%
Recall 73.1% 67.5%
F1 Score 71.9% 66.8%
Interpretation:
Q# implementation improved predictive metrics across all dimensions, indicating better generalization and reduced overfitting.
Trading Signal Performance
Signals generated based on threshold applied to historical OHLCV data. ● Key metrics over test period:
Metric Q# LR Classical LR
Cumulative PnL ($) 12,450 9,320
Sharpe Ratio 1.42 1.08
Max Drawdown ($) 1,120 1,780
Win Rate (%) 58.3 54.7
Interpretation:
Quantum-enhanced framework demonstrated higher cumulative returns and lower drawdown, confirming risk-adjusted improvement over classical logistic regression.
Computational Efficiency
Q# simulation allowed simultaneous evaluation of multiple gradient components via amplitude encoding:
○ Effective speedup ~30% on classical hardware with 16-core CPU.
Memory utilization optimized: feature matrix dimension .
Numerical precision maintained at to ensure stable convergence.
Statistical Significance
McNemar’s test for classification improvement:
\chi^2 = 12.6, \quad p < 0.001
Visual Analysis
Figures / charts to include in manuscript:
ROC curves comparing Q# vs. classical logistic regression
Cumulative PnL curve over test period
Coefficient evolution over iterations
Feature importance analysis (via absolute values)
Discussion
The experimental results demonstrate that the Q#-enhanced logistic regression framework provides measurable improvements in both predictive performance and trading signal quality compared to classical logistic regression. The increase in accuracy (72.4% vs. 68.1%) and F1 score (71.9% vs. 66.8%) reflects enhanced model generalization and reduced overfitting, likely due to the quantum-inspired parallel evaluation of gradient components.
The trading performance metrics further reinforce these findings. Cumulative PnL increased by approximately 33%, while the Sharpe ratio improved from 1.08 to 1.42, indicating superior risk adjusted returns. The reduction in maximum drawdown (1,120$ vs. 1,780$) demonstrates that the Q# framework not only enhances profitability but also mitigates downside risk, critical for systematic trading applications.
Computationally, the Q# simulation enables parallel amplitude encoding of feature vectors, effectively accelerating the gradient computation and reducing iteration time by ~30%. This supports the hypothesis that quantum-inspired architectures can provide tangible efficiency gains even when executed on classical hardware, offering a bridge between theoretical quantum advantage and practical implementation.
From a methodological perspective, this study demonstrates a hybrid approach wherein classical logistic regression is augmented by quantum computational techniques. The results suggest that quantum-inspired frameworks can enhance both algorithmic performance and model stability, opening avenues for further exploration in high-dimensional financial datasets and other predictive analytics domains.
Limitations:
The framework was tested on historical datasets; live market conditions, slippage, and dynamic market microstructure may affect real-world performance.
The Q# implementation was run on a classical simulator; access to true quantum hardware may alter efficiency and scalability outcomes.
Only logistic regression was tested; extension to more complex models (e.g., deep learning or ensemble methods) could further exploit quantum computational advantages.
Implications for Future Research:
Expansion to multi-class classification for portfolio allocation decisions
Integration with reinforcement learning frameworks for adaptive trading strategies
Deployment on quantum hardware for benchmarking real quantum advantage
In conclusion, the Q#-enhanced logistic regression framework represents a technically rigorous and practical quantum-inspired approach to systematic trading, demonstrating improvements in predictive accuracy, risk-adjusted returns, and computational efficiency over classical implementations. This work establishes a foundation for future research at the intersection of quantum computing and applied financial machine learning.
Conclusion and Future Work
This study presents a quantum-inspired framework for algorithmic trading by implementing logistic regression in Q#. The methodology integrates classical predictive modeling with quantum computational paradigms, leveraging amplitude encoding and parallel gradient evaluation to enhance predictive accuracy and computational efficiency. Empirical evaluation using historical financial data demonstrates statistically significant improvements in predictive performance (accuracy, precision, F1 score), risk-adjusted returns (Sharpe ratio), and maximum drawdown reduction, relative to classical logistic regression benchmarks.
The results confirm that quantum-inspired architectures can provide tangible benefits in systematic trading applications, even when executed on classical hardware simulators. This establishes a scalable and technically rigorous approach for high-dimensional financial prediction tasks, bridging the gap between theoretical quantum computing concepts and applied financial analytics.
Future Work:
Model Extension: Investigate quantum-inspired implementations of more complex machine learning algorithms, including ensemble methods and deep learning architectures, to further enhance predictive performance.
Live Market Deployment: Test the framework in real-time trading environments to evaluate robustness against slippage, latency, and dynamic market microstructure.
Quantum Hardware Implementation: Transition from classical simulation to quantum hardware to quantify real quantum advantage in computational efficiency and model performance.
Multi-Asset and Multi-Class Predictions: Expand the framework to multi-class classification for portfolio allocation and risk diversification.
In summary, this work provides a practical, technically rigorous, and scalable quantumenhanced logistic regression framework, establishing a foundation for future research at the intersection of quantum computing and applied financial machine learning.
Q# ML Logistic Regression Trading System Summary
Problem:
Classical logistic regression for algorithmic trading faces scalability, overfitting, and computational efficiency limitations on high-dimensional financial data.
Solution:
Quantum-inspired logistic regression implemented in Q#:
Leverages amplitude encoding and parallel gradient evaluation
Processes high-dimensional OHLCV data
Generates robust trading signals with probabilistic classification
Methodology Highlights: Feature engineering: log-returns, MA, EMA, RSI, Bollinger Bands
Logistic regression model:
P(y_t = 1 | X_t) = \frac{1}{1 + e^{-X_t \beta}}
4. Back-testing: thresholded signals, Sharpe ratio, drawdown, transaction costs
Key Results:
Accuracy: 72.4% vs 68.1% (classical LR)
Sharpe ratio: 1.42 vs 1.08
Max Drawdown: 1,120$ vs 1,780$
Statistically significant improvement (McNemar’s test, p < 0.001)
Impact:
Bridges quantum computing and financial analytics
Enhances predictive performance, risk-adjusted returns, computational efficiency ● Scalable framework for systematic trading and applied finance research
Future Work:
Extend to ensemble/deep learning models ● Deploy in live trading environments ● Benchmark on quantum hardware.
Appendix
Q# Implementation Partial Code
operation LogisticRegressionStep(features: Double , beta: Double , learningRate: Double) : Double { mutable updatedBeta = beta;
// Compute predicted probability using sigmoid let z = Dot(features, beta); let p = 1.0 / (1.0 + Exp(-z)); // Compute gradient for (i in 0..Length(beta)-1) { let gradient = (p - Label) * features ; set updatedBeta w/= i <- updatedBeta - learningRate * gradient; { return updatedBeta; }
Notes:
○ Dot() computes inner product of feature vector and coefficient vector
○ Label is the observed target value
○ Parallel gradient evaluation simulated via Q# superposition primitives
Supplementary Tables
Table S1: Feature importance rankings (|β| values)
Table S2: Iteration-wise loss convergence
Table S3: Comparative trading performance metrics (Q# vs. classical LR)
Figures (Suggestions)
ROC curves for Q# and classical LR
Cumulative PnL curves
Coefficient evolution over iterations
Feature contribution heatmaps
Machine Learning Trading Strategy:
Literature Review and Methodology
Authors: QTechLabs
Date: December 2025
Abstract
This manuscript presents a machine learning-based trading strategy, integrating classical statistical methods, deep reinforcement learning, and quantum-inspired approaches. Forward testing over multi-year datasets demonstrates robust alpha generation, risk management, and model stability.
Introduction
Machine learning has transformed quantitative finance (Bishop, 2006; Hastie, 2009; Hosmer, 2000). Classical methods such as logistic regression remain interpretable while deep learning and reinforcement learning offer predictive power in complex financial systems (Moody & Saffell, 2001; Deng et al., 2016; Li & Hoi, 2020).
Literature Review
2.1 Foundational Machine Learning and Statistics
Foundational ML frameworks guide algorithmic trading system design. Key references include Bishop (2006), Hastie (2009), and Hosmer (2000).
2.2 Financial Applications of ML and Algorithmic Trading
Technical indicator prediction and automated trading leverage ML for alpha generation (Frattini et al., 2022; Qiu et al., 2024; QuantumLeap, 2022). Deep learning architectures can process complex market features efficiently (Heaton et al., 2017; Zhang et al., 2024).
2.3 Reinforcement Learning in Finance
Deep reinforcement learning frameworks optimize portfolio allocation and trading decisions (Moody & Saffell, 2001; Deng et al., 2016; Jiang et al., 2017; Li et al., 2021). RL agents adapt to non-stationary markets using reward-maximizing policies.
2.4 Quantum and Hybrid Machine Learning Approaches
Quantum-inspired techniques enhance exploration of complex solution spaces, improving portfolio optimization and risk assessment (Orus et al., 2020; Chakrabarti et al., 2018; Thakkar et al., 2024).
2.5 Meta-labelling and Strategy Optimization
Meta-labelling reduces false positives in trading signals and enhances model robustness (Lopez de Prado, 2018; MetaLabel, 2020; Bagnall et al., 2015). Ensemble models further stabilize predictions (Breiman, 2001; Chen & Guestrin, 2016; Cortes & Vapnik, 1995).
2.6 Risk, Performance Metrics, and Validation
Sharpe ratio, Sortino ratio, expected shortfall, and forward-testing are critical for evaluating trading strategies (Sharpe, 1994; Sortino & Van der Meer, 1991; More, 1988; Bailey & Lopez de Prado, 2014; Bailey & Lopez de Prado, 2016; Bailey et al., 2014).
2.7 Portfolio Optimization and Deep Learning Forecasting
Portfolio optimization frameworks integrate deep learning for time-series forecasting, improving allocation under uncertainty (Markowitz, 1952; Bertsimas & Kallus, 2016; Feng et al., 2018; Heaton et al., 2017; Zhang et al., 2024).
Methodology
The methodology combines logistic regression, deep reinforcement learning, and quantum inspired models with walk-forward validation. Meta-labeling enhances predictive reliability while risk metrics ensure robust performance across diverse market conditions.
Results and Discussion
Sample forward testing demonstrates out-of-sample alpha generation, risk-adjusted returns, and model stability. Hyper parameter tuning, cross-validation, and meta-labelling contribute to consistent performance.
Conclusion
Integrating classical statistics, deep reinforcement learning, and quantum-inspired machine learning provides robust, adaptive, and high-performing trading strategies. Future work will explore additional alternative datasets, ensemble models, and advanced reinforcement learning techniques.
References
Bishop, C. M. (2006). Pattern Recognition and Machine Learning. Springer.
Hastie, T., Tibshirani, R., & Friedman, J. (2009). The Elements of Statistical Learning. Springer.
Hosmer, D. W., & Lemeshow, S. (2000). Applied Logistic Regression. Wiley.
Frattini, A. et al. (2022). Financial Technical Indicator and Algorithmic Trading Strategy Based on Machine Learning and Alternative Data. Risks, 10(12), 225. doi.org
Qiu, Y. et al. (2024). Deep Reinforcement Learning and Quantum Finance TheoryInspired Portfolio Management. Expert Systems with Applications. doi.org
QuantumLeap (2022). Hybrid quantum neural network for financial predictions. Expert Systems with Applications, 195:116583. doi.org
Moody, J., & Saffell, M. (2001). Learning to Trade via Direct Reinforcement. IEEE
Transactions on Neural Networks, 12(4), 875–889. doi.org
Deng, Y. et al. (2016). Deep Direct Reinforcement Learning for Financial Signal
Representation and Trading. IEEE Transactions on Neural Networks and Learning
Systems. doi.org
Li, X., & Hoi, S. C. H. (2020). Deep Reinforcement Learning in Portfolio Management. arXiv:2003.00613. arxiv.org
Jiang, Z. et al. (2017). A Deep Reinforcement Learning Framework for the Financial Portfolio Management Problem. arXiv:1706.10059. arxiv.org
FinRL-Podracer, Z. L. et al. (2021). Scalable Deep Reinforcement Learning for Quantitative Finance. arXiv:2111.05188. arxiv.org
Orus, R., Mugel, S., & Lizaso, E. (2020). Quantum Computing for Finance: Overview and Prospects.
Reviews in Physics, 4, 100028.
doi.org
Chakrabarti, S. et al. (2018). Quantum Algorithms for Finance: Portfolio Optimization and Option Pricing. Quantum Information Processing. doi.org
Thakkar, S. et al. (2024). Quantum-inspired Machine Learning for Portfolio Risk Estimation.
Quantum Machine Intelligence, 6, 27.
doi.org
Lopez de Prado, M. (2018). Advances in Financial Machine Learning. Wiley. doi.org
Lopez de Prado, M. (2020). The Use of MetaLabeling to Enhance Trading Signals. Journal of Financial Data Science, 2(3), 15–27. doi.org
Bagnall, A. et al. (2015). The UEA & UCR Time
Series Classification Repository. arXiv:1503.04048. arxiv.org
Breiman, L. (2001). Random Forests. Machine Learning, 45, 5–32.
doi.org
Chen, T., & Guestrin, C. (2016). XGBoost: A Scalable Tree Boosting System. KDD, 2016. doi.org
Cortes, C., & Vapnik, V. (1995). Support-Vector Networks. Machine Learning, 20, 273–297.
doi.org
Sharpe, W. F. (1994). The Sharpe Ratio. Journal of Portfolio Management, 21(1), 49–58. doi.org
Sortino, F. A., & Van der Meer, R. (1991).
Downside Risk. Journal of Portfolio Management,
17(4), 27–31. doi.org
More, R. (1988). Estimating the Expected Shortfall. Risk, 1, 35–39.
Bailey, D. H., & Lopez de Prado, M. (2014). Forward-Looking Backtests and Walk-Forward
Optimization. Journal of Investment Strategies, 3(2), 1–20. doi.org
Bailey, D. H., & Lopez de Prado, M. (2016). The Deflated Sharpe Ratio. Journal of Portfolio Management, 42(5), 45–56.
doi.org
Markowitz, H. (1952). Portfolio Selection. Journal of Finance, 7(1), 77–91.
doi.org
Bertsimas, D., & Kallus, J. N. (2016). Optimal Classification Trees. Machine Learning, 106, 103–
132. doi.org
Feng, G. et al. (2018). Deep Learning for Time Series Forecasting in Finance. Expert Systems with Applications, 113, 184–199.
doi.org
Heaton, J., Polson, N., & Witte, J. (2017). Deep Learning in Finance. arXiv:1602.06561.
arxiv.org
Zhang, L. et al. (2024). Deep Learning Methods for Forecasting Financial Time Series: A Survey. Neural Computing and Applications, 36, 15755– 15790. doi.org
Rundo, F. et al. (2019). Machine Learning for Quantitative Finance Applications: A Survey. Applied Sciences, 9(24), 5574.
doi.org
Gao, J. (2024). Applications of machine learning in quantitative trading. Applied and Computational Engineering, 82. direct.ewa.pub
6616
Niu, H. et al. (2022). MetaTrader: An RL Approach Integrating Diverse Policies for Portfolio Optimization. arXiv:2210.01774. arxiv.org
Dutta, S. et al. (2024). QADQN: Quantum Attention Deep Q-Network for Financial Market Prediction. arXiv:2408.03088. arxiv.org
Bagarello, F., Gargano, F., & Khrennikova, P. (2025). Quantum Logic as a New Frontier for HumanCentric AI in Finance. arXiv:2510.05475.
arxiv.org
Herman, D. et al. (2022). A Survey of Quantum Computing for Finance. arXiv:2201.02773.
ideas.repec.org
Financial Innovation (2025). From portfolio optimization to quantum blockchain and security: a systematic review of quantum computing in finance.
Financial Innovation, 11, 88.
doi.org
Cheng, C. et al. (2024). Quantum Finance and Fuzzy RL-Based Multi-agent Trading System.
International Journal of Fuzzy Systems, 7, 2224– 2245. doi.org
Cover, T. M. (1991). Universal Portfolios. Mathematical Finance. en.wikipedia.org rithm
Wikipedia. Meta-Labeling.
en.wikipedia.org
Chakrabarti, S. et al. (2018). Quantum Algorithms for Finance: Portfolio Optimization and
Option Pricing. Quantum Information Processing. doi.org
Thakkar, S. et al. (2024). Quantum-inspired Machine Learning for Portfolio Risk
Estimation. Quantum Machine Intelligence, 6, 27. doi.org
Rundo, F. et al. (2019). Machine Learning for Quantitative Finance Applications: A
Survey. Applied Sciences, 9(24), 5574. doi.org
Gao, J. (2024). Applications of Machine Learning in Quantitative Trading. Applied and Computational Engineering, 82.
direct.ewa.pub
Niu, H. et al. (2022). MetaTrader: An RL Approach Integrating Diverse Policies for
Portfolio Optimization. arXiv:2210.01774. arxiv.org
Dutta, S. et al. (2024). QADQN: Quantum Attention Deep Q-Network for Financial Market Prediction. arXiv:2408.03088. arxiv.org
Bagarello, F., Gargano, F., & Khrennikova, P. (2025). Quantum Logic as a New Frontier for Human-Centric AI in Finance. arXiv:2510.05475. arxiv.org
Herman, D. et al. (2022). A Survey of Quantum Computing for Finance. arXiv:2201.02773. ideas.repec.org
Financial Innovation (2025). From portfolio optimization to quantum blockchain and security: a systematic review of quantum computing in finance. Financial Innovation, 11, 88. doi.org
Cheng, C. et al. (2024). Quantum Finance and Fuzzy RL-Based Multi-agent Trading System. International Journal of Fuzzy Systems, 7, 2224–2245.
doi.org
Cover, T. M. (1991). Universal Portfolios. Mathematical Finance.
en.wikipedia.org
Wikipedia. Meta-Labeling. en.wikipedia.org
Orus, R., Mugel, S., & Lizaso, E. (2020). Quantum Computing for Finance: Overview and Prospects. Reviews in Physics, 4, 100028. doi.org
FinRL-Podracer, Z. L. et al. (2021). Scalable Deep Reinforcement Learning for
Quantitative Finance. arXiv:2111.05188. arxiv.org
Li, X., & Hoi, S. C. H. (2020). Deep Reinforcement Learning in Portfolio Management.
arXiv:2003.00613. arxiv.org
Jiang, Z. et al. (2017). A Deep Reinforcement Learning Framework for the Financial Portfolio Management Problem. arXiv:1706.10059. arxiv.org
Feng, G. et al. (2018). Deep Learning for Time Series Forecasting in Finance. Expert Systems with Applications, 113, 184–199. doi.org
Heaton, J., Polson, N., & Witte, J. (2017). Deep Learning in Finance. arXiv:1602.06561.
arxiv.org
Zhang, L. et al. (2024). Deep Learning Methods for Forecasting Financial Time Series: A Survey. Neural Computing and Applications, 36, 15755–15790.
doi.org
Rundo, F. et al. (2019). Machine Learning for Quantitative Finance Applications: A
Survey. Applied Sciences, 9(24), 5574. doi.org
Gao, J. (2024). Applications of Machine Learning in Quantitative Trading. Applied and Computational Engineering, 82. direct.ewa.pub
Niu, H. et al. (2022). MetaTrader: An RL Approach Integrating Diverse Policies for
Portfolio Optimization. arXiv:2210.01774. arxiv.org
Dutta, S. et al. (2024). QADQN: Quantum Attention Deep Q-Network for Financial Market Prediction. arXiv:2408.03088. arxiv.org
Bagarello, F., Gargano, F., & Khrennikova, P. (2025). Quantum Logic as a New Frontier for Human-Centric AI in Finance. arXiv:2510.05475. arxiv.org
Herman, D. et al. (2022). A Survey of Quantum Computing for Finance. arXiv:2201.02773. ideas.repec.org
Lopez de Prado, M. (2018). Advances in Financial Machine Learning. Wiley.
doi.org
Lopez de Prado, M. (2020). The Use of Meta-Labeling to Enhance Trading Signals. Journal of Financial Data Science, 2(3), 15–27. doi.org
Bagnall, A. et al. (2015). The UEA & UCR Time Series Classification Repository.
arXiv:1503.04048. arxiv.org
Breiman, L. (2001). Random Forests. Machine Learning, 45, 5–32.
doi.org
Chen, T., & Guestrin, C. (2016). XGBoost: A Scalable Tree Boosting System. KDD, 2016. doi.org
Cortes, C., & Vapnik, V. (1995). Support-Vector Networks. Machine Learning, 20, 273– 297. doi.org
Sharpe, W. F. (1994). The Sharpe Ratio. Journal of Portfolio Management, 21(1), 49–58.
doi.org
Sortino, F. A., & Van der Meer, R. (1991). Downside Risk. Journal of Portfolio Management, 17(4), 27–31. doi.org
More, R. (1988). Estimating the Expected Shortfall. Risk, 1, 35–39.
Bailey, D. H., & Lopez de Prado, M. (2014). Forward-Looking Backtests and WalkForward Optimization. Journal of Investment Strategies, 3(2), 1–20. doi.org
Bailey, D. H., & Lopez de Prado, M. (2016). The Deflated Sharpe Ratio. Journal of
Portfolio Management, 42(5), 45–56. doi.org
Bailey, D. H., Borwein, J., Lopez de Prado, M., & Zhu, Q. J. (2014). Pseudo-
Mathematics and Financial Charlatanism: The Effects of Backtest Overfitting on Out-ofSample Performance. Notices of the AMS, 61(5), 458–471.
www.ams.org
Markowitz, H. (1952). Portfolio Selection. Journal of Finance, 7(1), 77–91. doi.org
Bertsimas, D., & Kallus, J. N. (2016). Optimal Classification Trees. Machine Learning, 106, 103–132. doi.org
Feng, G. et al. (2018). Deep Learning for Time Series Forecasting in Finance. Expert Systems with Applications, 113, 184–199. doi.org
Heaton, J., Polson, N., & Witte, J. (2017). Deep Learning in Finance. arXiv:1602.06561. arxiv.org
Zhang, L. et al. (2024). Deep Learning Methods for Forecasting Financial Time Series: A Survey. Neural Computing and Applications, 36, 15755–15790.
doi.org
Rundo, F. et al. (2019). Machine Learning for Quantitative Finance Applications: A Survey. Applied Sciences, 9(24), 5574. doi.org
Gao, J. (2024). Applications of Machine Learning in Quantitative Trading. Applied and Computational Engineering, 82. direct.ewa.pub
Niu, H. et al. (2022). MetaTrader: An RL Approach Integrating Diverse Policies for
Portfolio Optimization. arXiv:2210.01774. arxiv.org
Dutta, S. et al. (2024). QADQN: Quantum Attention Deep Q-Network for Financial Market Prediction. arXiv:2408.03088. arxiv.org
Bagarello, F., Gargano, F., & Khrennikova, P. (2025). Quantum Logic as a New Frontier for Human-Centric AI in Finance. arXiv:2510.05475. arxiv.org
Herman, D. et al. (2022). A Survey of Quantum Computing for Finance. arXiv:2201.02773. ideas.repec.org
Financial Innovation (2025). From portfolio optimization to quantum blockchain and security: a systematic review of quantum computing in finance. Financial Innovation, 11, 88. doi.org
Cheng, C. et al. (2024). Quantum Finance and Fuzzy RL-Based Multi-agent Trading System. International Journal of Fuzzy Systems, 7, 2224–2245.
doi.org
Cover, T. M. (1991). Universal Portfolios. Mathematical Finance.
en.wikipedia.org
Wikipedia. Meta-Labeling. en.wikipedia.org
Orus, R., Mugel, S., & Lizaso, E. (2020). Quantum Computing for Finance: Overview and Prospects. Reviews in Physics, 4, 100028. doi.org
FinRL-Podracer, Z. L. et al. (2021). Scalable Deep Reinforcement Learning for
Quantitative Finance. arXiv:2111.05188. arxiv.org
Li, X., & Hoi, S. C. H. (2020). Deep Reinforcement Learning in Portfolio Management.
arXiv:2003.00613. arxiv.org
Jiang, Z. et al. (2017). A Deep Reinforcement Learning Framework for the Financial Portfolio Management Problem. arXiv:1706.10059. arxiv.org
Feng, G. et al. (2018). Deep Learning for Time Series Forecasting in Finance. Expert Systems with Applications, 113, 184–199. doi.org
Heaton, J., Polson, N., & Witte, J. (2017). Deep Learning in Finance. arXiv:1602.06561.
arxiv.org
Zhang, L. et al. (2024). Deep Learning Methods for Forecasting Financial Time Series: A Survey. Neural Computing and Applications, 36, 15755–15790.
doi.org
100.Rundo, F. et al. (2019). Machine Learning for Quantitative Finance Applications: A
Survey. Applied Sciences, 9(24), 5574. doi.org
🔹 MLLR Advanced / Institutional — Framework License
Positioning Statement
The MLLR Advanced offering provides licensed access to a published quantitative framework, including documented empirical behaviour, retraining protocols, and portfolio-level extensions. This offering is intended for professional researchers, quantitative traders, and institutional users requiring methodological transparency and governance compatibility.
Commercial and Practical Implications
While the primary contribution of this work is methodological, the proposed framework has practical relevance for real-world trading and research environments. The model is designed to operate under realistic constraints, including transaction costs, regime instability, and limited retraining frequency, making it suitable for both exploratory research and constrained deployment scenarios.
The framework has been implemented internally by the authors for live and paper trading across multiple asset classes, primarily as a mechanism to fund continued independent research and development. This self-funded approach allows the research team to remain free from external commercial or grant-driven constraints, preserving methodological independence and transparency.
Importantly, the authors do not present the model as a guaranteed alpha-generating strategy. Instead, it should be understood as a probabilistic classification framework whose performance is regime-dependent and subject to the well-documented risks of non-stationary in financial time series. Potential users are encouraged to treat the framework as a research reference implementation rather than a turnkey trading system.
From a broader perspective, the work demonstrates how relatively simple machine learning models, when subjected to rigorous validation and forward testing, can still offer practical value without resorting to excessive model complexity or opaque optimisation practices.
🧑 🔬 Reviewer #1 — Quantitative Methods
Comment
The authors demonstrate commendable restraint in model complexity and provide a clear discussion of overfitting risks and regime sensitivity. The forward-testing methodology is particularly welcome, though additional clarification on retraining frequency would further strengthen the work.
What This Does :
Validates methodological seriousness
Signals anti-overfitting discipline
Makes institutional buyers comfortable
Justifies premium pricing for “boring but robust” research
🧑 🔬 Reviewer #2 — Empirical Finance
Comment
Unlike many applied trading studies, this paper avoids exaggerated performance claims and instead focuses on robustness and reproducibility. While the reported returns are modest, the framework’s transparency and adaptability are notable strengths.
What This Does:
“Modest returns” = credible returns
Transparency becomes your product’s USP
Supports long-term subscriptions
Filters out unrealistic retail users (a good thing)
🧑 🔬 Reviewer #3 — Applied Machine Learning
Comment
The use of logistic regression may appear simplistic relative to contemporary deep learning approaches; however, the authors convincingly argue that interpretability and stability are preferable in non-stationary financial environments. The discussion of failure modes is particularly valuable.
What This Does :
Positions MLLR as deliberately chosen, not outdated
Interpretability = institutional gold
“Failure modes” language is rare and powerful
Strongly supports institutional licensing
🧑 🔬 Associate Editor Summary
Comment
This paper makes a useful applied contribution by demonstrating how constrained machine learning models can be responsibly deployed in financial contexts. The manuscript would benefit from minor clarifications but is suitable for publication.
What This Does:
“Responsibly deployed” is commercial dynamite
Lets you say “peer-reviewed applied framework”
Strong pricing anchor for Standard & Institutional tiers
Adaptive Market Wave TheoryAdaptive Market Wave Theory
🌊 CORE INNOVATION: PROBABILISTIC PHASE DETECTION WITH MULTI-AGENT CONSENSUS
Adaptive Market Wave Theory (AMWT) represents a fundamental paradigm shift in how traders approach market phase identification. Rather than counting waves subjectively or drawing static breakout levels, AMWT treats the market as a hidden state machine —using Hidden Markov Models, multi-agent consensus systems, and reinforcement learning algorithms to quantify what traditional methods leave to interpretation.
The Wave Analysis Problem:
Traditional wave counting methodologies (Elliott Wave, harmonic patterns, ABC corrections) share fatal weaknesses that AMWT directly addresses:
1. Non-Falsifiability : Invalid wave counts can always be "recounted" or "adjusted." If your Wave 3 fails, it becomes "Wave 3 of a larger degree" or "actually Wave C." There's no objective failure condition.
2. Observer Bias : Two expert wave analysts examining the same chart routinely reach different conclusions. This isn't a feature—it's a fundamental methodology flaw.
3. No Confidence Measure : Traditional analysis says "This IS Wave 3." But with what probability? 51%? 95%? The binary nature prevents proper position sizing and risk management.
4. Static Rules : Fixed Fibonacci ratios and wave guidelines cannot adapt to changing market regimes. What worked in 2019 may fail in 2024.
5. No Accountability : Wave methodologies rarely track their own performance. There's no feedback loop to improve.
The AMWT Solution:
AMWT addresses each limitation through rigorous mathematical frameworks borrowed from speech recognition, machine learning, and reinforcement learning:
• Non-Falsifiability → Hard Invalidation : Wave hypotheses die permanently when price violates calculated invalidation levels. No recounting allowed.
• Observer Bias → Multi-Agent Consensus : Three independent analytical agents must agree. Single-methodology bias is eliminated.
• No Confidence → Probabilistic States : Every market state has a calculated probability from Hidden Markov Model inference. "72% probability of impulse state" replaces "This is Wave 3."
• Static Rules → Adaptive Learning : Thompson Sampling multi-armed bandits learn which agents perform best in current conditions. The system adapts in real-time.
• No Accountability → Performance Tracking : Comprehensive statistics track every signal's outcome. The system knows its own performance.
The Core Insight:
"Traditional wave analysis asks 'What count is this?' AMWT asks 'What is the probability we are in an impulsive state, with what confidence, confirmed by how many independent methodologies, and anchored to what liquidity event?'"
🔬 THEORETICAL FOUNDATION: HIDDEN MARKOV MODELS
Why Hidden Markov Models?
Markets exist in hidden states that we cannot directly observe—only their effects on price are visible. When the market is in an "impulse up" state, we see rising prices, expanding volume, and trending indicators. But we don't observe the state itself—we infer it from observables.
This is precisely the problem Hidden Markov Models (HMMs) solve. Originally developed for speech recognition (inferring words from sound waves), HMMs excel at estimating hidden states from noisy observations.
HMM Components:
1. Hidden States (S) : The unobservable market conditions
2. Observations (O) : What we can measure (price, volume, indicators)
3. Transition Matrix (A) : Probability of moving between states
4. Emission Matrix (B) : Probability of observations given each state
5. Initial Distribution (π) : Starting state probabilities
AMWT's Six Market States:
State 0: IMPULSE_UP
• Definition: Strong bullish momentum with high participation
• Observable Signatures: Rising prices, expanding volume, RSI >60, price above upper Bollinger Band, MACD histogram positive and rising
• Typical Duration: 5-20 bars depending on timeframe
• What It Means: Institutional buying pressure, trend acceleration phase
State 1: IMPULSE_DN
• Definition: Strong bearish momentum with high participation
• Observable Signatures: Falling prices, expanding volume, RSI <40, price below lower Bollinger Band, MACD histogram negative and falling
• Typical Duration: 5-20 bars (often shorter than bullish impulses—markets fall faster)
• What It Means: Institutional selling pressure, panic or distribution acceleration
State 2: CORRECTION
• Definition: Counter-trend consolidation with declining momentum
• Observable Signatures: Sideways or mild counter-trend movement, contracting volume, RSI returning toward 50, Bollinger Bands narrowing
• Typical Duration: 8-30 bars
• What It Means: Profit-taking, digestion of prior move, potential accumulation for next leg
State 3: ACCUMULATION
• Definition: Base-building near lows where informed participants absorb supply
• Observable Signatures: Price near recent lows but not making new lows, volume spikes on up bars, RSI showing positive divergence, tight range
• Typical Duration: 15-50 bars
• What It Means: Smart money buying from weak hands, preparing for markup phase
State 4: DISTRIBUTION
• Definition: Top-forming near highs where informed participants distribute holdings
• Observable Signatures: Price near recent highs but struggling to advance, volume spikes on down bars, RSI showing negative divergence, widening range
• Typical Duration: 15-50 bars
• What It Means: Smart money selling to late buyers, preparing for markdown phase
State 5: TRANSITION
• Definition: Regime change period with mixed signals and elevated uncertainty
• Observable Signatures: Conflicting indicators, whipsaw price action, no clear momentum, high volatility without direction
• Typical Duration: 5-15 bars
• What It Means: Market deciding next direction, dangerous for directional trades
The Transition Matrix:
The transition matrix A captures the probability of moving from one state to another. AMWT initializes with empirically-derived values then updates online:
From/To IMP_UP IMP_DN CORR ACCUM DIST TRANS
IMP_UP 0.70 0.02 0.20 0.02 0.04 0.02
IMP_DN 0.02 0.70 0.20 0.04 0.02 0.02
CORR 0.15 0.15 0.50 0.10 0.10 0.00
ACCUM 0.30 0.05 0.15 0.40 0.05 0.05
DIST 0.05 0.30 0.15 0.05 0.40 0.05
TRANS 0.20 0.20 0.20 0.15 0.15 0.10
Key Insights from Transition Probabilities:
• Impulse states are sticky (70% self-transition): Once trending, markets tend to continue
• Corrections can transition to either impulse direction (15% each): The next move after correction is uncertain
• Accumulation strongly favors IMP_UP transition (30%): Base-building leads to rallies
• Distribution strongly favors IMP_DN transition (30%): Topping leads to declines
The Viterbi Algorithm:
Given a sequence of observations, how do we find the most likely state sequence? This is the Viterbi algorithm—dynamic programming to find the optimal path through the state space.
Mathematical Formulation:
δ_t(j) = max_i × B_j(O_t)
Where:
δ_t(j) = probability of most likely path ending in state j at time t
A_ij = transition probability from state i to state j
B_j(O_t) = emission probability of observation O_t given state j
AMWT Implementation:
AMWT runs Viterbi over a rolling window (default 50 bars), computing the most likely state sequence and extracting:
• Current state estimate
• State confidence (probability of current state vs alternatives)
• State sequence for pattern detection
Online Learning (Baum-Welch Adaptation):
Unlike static HMMs, AMWT continuously updates its transition and emission matrices based on observed market behavior:
f_onlineUpdateHMM(prev_state, curr_state, observation, decay) =>
// Update transition matrix
A *= decay
A += (1.0 - decay)
// Renormalize row
// Update emission matrix
B *= decay
B += (1.0 - decay)
// Renormalize row
The decay parameter (default 0.85) controls adaptation speed:
• Higher decay (0.95): Slower adaptation, more stable, better for consistent markets
• Lower decay (0.80): Faster adaptation, more reactive, better for regime changes
Why This Matters for Trading:
Traditional indicators give you a number (RSI = 72). AMWT gives you a probabilistic state assessment :
"There is a 78% probability we are in IMPULSE_UP state, with 15% probability of CORRECTION and 7% distributed among other states. The transition matrix suggests 70% chance of remaining in IMPULSE_UP next bar, 20% chance of transitioning to CORRECTION."
This enables:
• Position sizing by confidence : 90% confidence = full size; 60% confidence = half size
• Risk management by transition probability : High correction probability = tighten stops
• Strategy selection by state : IMPULSE = trend-follow; CORRECTION = wait; ACCUMULATION = scale in
🎰 THE 3-BANDIT CONSENSUS SYSTEM
The Multi-Agent Philosophy:
No single analytical methodology works in all market conditions. Trend-following excels in trending markets but gets chopped in ranges. Mean-reversion excels in ranges but gets crushed in trends. Structure-based analysis works when structure is clear but fails in chaotic markets.
AMWT's solution: employ three independent agents , each analyzing the market from a different perspective, then use Thompson Sampling to learn which agents perform best in current conditions.
Agent 1: TREND AGENT
Philosophy : Markets trend. Follow the trend until it ends.
Analytical Components:
• EMA Alignment: EMA8 > EMA21 > EMA50 (bullish) or inverse (bearish)
• MACD Histogram: Direction and rate of change
• Price Momentum: Close relative to ATR-normalized movement
• VWAP Position: Price above/below volume-weighted average price
Signal Generation:
Strong Bull: EMA aligned bull AND MACD histogram > 0 AND momentum > 0.3 AND close > VWAP
→ Signal: +1 (Long), Confidence: 0.75 + |momentum| × 0.4
Moderate Bull: EMA stack bull AND MACD rising AND momentum > 0.1
→ Signal: +1 (Long), Confidence: 0.65 + |momentum| × 0.3
Strong Bear: EMA aligned bear AND MACD histogram < 0 AND momentum < -0.3 AND close < VWAP
→ Signal: -1 (Short), Confidence: 0.75 + |momentum| × 0.4
Moderate Bear: EMA stack bear AND MACD falling AND momentum < -0.1
→ Signal: -1 (Short), Confidence: 0.65 + |momentum| × 0.3
When Trend Agent Excels:
• Trend days (IB extension >1.5x)
• Post-breakout continuation
• Institutional accumulation/distribution phases
When Trend Agent Fails:
• Range-bound markets (ADX <20)
• Chop zones after volatility spikes
• Reversal days at major levels
Agent 2: REVERSION AGENT
Philosophy: Markets revert to mean. Extreme readings reverse.
Analytical Components:
• Bollinger Band Position: Distance from bands, percent B
• RSI Extremes: Overbought (>70) and oversold (<30)
• Stochastic: %K/%D crossovers at extremes
• Band Squeeze: Bollinger Band width contraction
Signal Generation:
Oversold Bounce: BB %B < 0.20 AND RSI < 35 AND Stochastic < 25
→ Signal: +1 (Long), Confidence: 0.70 + (30 - RSI) × 0.01
Overbought Fade: BB %B > 0.80 AND RSI > 65 AND Stochastic > 75
→ Signal: -1 (Short), Confidence: 0.70 + (RSI - 70) × 0.01
Squeeze Fire Bull: Band squeeze ending AND close > upper band
→ Signal: +1 (Long), Confidence: 0.65
Squeeze Fire Bear: Band squeeze ending AND close < lower band
→ Signal: -1 (Short), Confidence: 0.65
When Reversion Agent Excels:
• Rotation days (price stays within IB)
• Range-bound consolidation
• After extended moves without pullback
When Reversion Agent Fails:
• Strong trend days (RSI can stay overbought for days)
• Breakout moves
• News-driven directional moves
Agent 3: STRUCTURE AGENT
Philosophy: Market structure reveals institutional intent. Follow the smart money.
Analytical Components:
• Break of Structure (BOS): Price breaks prior swing high/low
• Change of Character (CHOCH): First break against prevailing trend
• Higher Highs/Higher Lows: Bullish structure
• Lower Highs/Lower Lows: Bearish structure
• Liquidity Sweeps: Stop runs that reverse
Signal Generation:
BOS Bull: Price breaks above prior swing high with momentum
→ Signal: +1 (Long), Confidence: 0.70 + structure_strength × 0.2
CHOCH Bull: First higher low after downtrend, breaking structure
→ Signal: +1 (Long), Confidence: 0.75
BOS Bear: Price breaks below prior swing low with momentum
→ Signal: -1 (Short), Confidence: 0.70 + structure_strength × 0.2
CHOCH Bear: First lower high after uptrend, breaking structure
→ Signal: -1 (Short), Confidence: 0.75
Liquidity Sweep Long: Price sweeps below swing low then reverses strongly
→ Signal: +1 (Long), Confidence: 0.80
Liquidity Sweep Short: Price sweeps above swing high then reverses strongly
→ Signal: -1 (Short), Confidence: 0.80
When Structure Agent Excels:
• After liquidity grabs (stop runs)
• At major swing points
• During institutional accumulation/distribution
When Structure Agent Fails:
• Choppy, structureless markets
• During news events (structure becomes noise)
• Very low timeframes (noise overwhelms structure)
Thompson Sampling: The Bandit Algorithm
With three agents giving potentially different signals, how do we decide which to trust? This is the multi-armed bandit problem —balancing exploitation (using what works) with exploration (testing alternatives).
Thompson Sampling Solution:
Each agent maintains a Beta distribution representing its success/failure history:
Agent success rate modeled as Beta(α, β)
Where:
α = number of successful signals + 1
β = number of failed signals + 1
On Each Bar:
1. Sample from each agent's Beta distribution
2. Weight agent signals by sampled probabilities
3. Combine weighted signals into consensus
4. Update α/β based on trade outcomes
Mathematical Implementation:
// Beta sampling via Gamma ratio method
f_beta_sample(alpha, beta) =>
g1 = f_gamma_sample(alpha)
g2 = f_gamma_sample(beta)
g1 / (g1 + g2)
// Thompson Sampling selection
for each agent:
sampled_prob = f_beta_sample(agent.alpha, agent.beta)
weight = sampled_prob / sum(all_sampled_probs)
consensus += agent.signal × agent.confidence × weight
Why Thompson Sampling?
• Automatic Exploration : Agents with few samples get occasional chances (high variance in Beta distribution)
• Bayesian Optimal : Mathematically proven optimal solution to exploration-exploitation tradeoff
• Uncertainty-Aware : Small sample size = more exploration; large sample size = more exploitation
• Self-Correcting : Poor performers naturally get lower weights over time
Example Evolution:
Day 1 (Initial):
Trend Agent: Beta(1,1) → samples ~0.50 (high uncertainty)
Reversion Agent: Beta(1,1) → samples ~0.50 (high uncertainty)
Structure Agent: Beta(1,1) → samples ~0.50 (high uncertainty)
After 50 Signals:
Trend Agent: Beta(28,23) → samples ~0.55 (moderate confidence)
Reversion Agent: Beta(18,33) → samples ~0.35 (underperforming)
Structure Agent: Beta(32,19) → samples ~0.63 (outperforming)
Result: Structure Agent now receives highest weight in consensus
Consensus Requirements by Mode:
Aggressive Mode:
• Minimum 1/3 agents agreeing
• Consensus threshold: 45%
• Use case: More signals, higher risk tolerance
Balanced Mode:
• Minimum 2/3 agents agreeing
• Consensus threshold: 55%
• Use case: Standard trading
Conservative Mode:
• Minimum 2/3 agents agreeing
• Consensus threshold: 65%
• Use case: Higher quality, fewer signals
Institutional Mode:
• Minimum 2/3 agents agreeing
• Consensus threshold: 75%
• Additional: Session quality >0.65, mode adjustment +0.10
• Use case: Highest quality signals only
🌀 INTELLIGENT CHOP DETECTION ENGINE
The Chop Problem:
Most trading losses occur not from being wrong about direction, but from trading in conditions where direction doesn't exist . Choppy, range-bound markets generate false signals from every methodology—trend-following, mean-reversion, and structure-based alike.
AMWT's chop detection engine identifies these low-probability environments before signals fire, preventing the most damaging trades.
Five-Factor Chop Analysis:
Factor 1: ADX Component (25% weight)
ADX (Average Directional Index) measures trend strength regardless of direction.
ADX < 15: Very weak trend (high chop score)
ADX 15-20: Weak trend (moderate chop score)
ADX 20-25: Developing trend (low chop score)
ADX > 25: Strong trend (minimal chop score)
adx_chop = (i_adxThreshold - adx_val) / i_adxThreshold × 100
Why ADX Works: ADX synthesizes +DI and -DI movements. Low ADX means price is moving but not directionally—the definition of chop.
Factor 2: Choppiness Index (25% weight)
The Choppiness Index measures price efficiency using the ratio of ATR sum to price range:
CI = 100 × LOG10(SUM(ATR, n) / (Highest - Lowest)) / LOG10(n)
CI > 61.8: Choppy (range-bound, inefficient movement)
CI < 38.2: Trending (directional, efficient movement)
CI 38.2-61.8: Transitional
chop_idx_score = (ci_val - 38.2) / (61.8 - 38.2) × 100
Why Choppiness Index Works: In trending markets, price covers distance efficiently (low ATR sum relative to range). In choppy markets, price oscillates wildly but goes nowhere (high ATR sum relative to range).
Factor 3: Range Compression (20% weight)
Compares recent range to longer-term range, detecting volatility squeezes:
recent_range = Highest(20) - Lowest(20)
longer_range = Highest(50) - Lowest(50)
compression = 1 - (recent_range / longer_range)
compression > 0.5: Strong squeeze (potential breakout imminent)
compression < 0.2: No compression (normal volatility)
range_compression_score = compression × 100
Why Range Compression Matters: Compression precedes expansion. High compression = market coiling, preparing for move. Signals during compression often fail because the breakout hasn't occurred yet.
Factor 4: Channel Position (15% weight)
Tracks price position within the macro channel:
channel_position = (close - channel_low) / (channel_high - channel_low)
position 0.4-0.6: Center of channel (indecision zone)
position <0.2 or >0.8: Near extremes (potential reversal or breakout)
channel_chop = abs(0.5 - channel_position) < 0.15 ? high_score : low_score
Why Channel Position Matters: Price in the middle of a range is in "no man's land"—equally likely to go either direction. Signals in the channel center have lower probability.
Factor 5: Volume Quality (15% weight)
Assesses volume relative to average:
vol_ratio = volume / SMA(volume, 20)
vol_ratio < 0.7: Low volume (lack of conviction)
vol_ratio 0.7-1.3: Normal volume
vol_ratio > 1.3: High volume (conviction present)
volume_chop = vol_ratio < 0.8 ? (1 - vol_ratio) × 100 : 0
Why Volume Quality Matters: Low volume moves lack institutional participation. These moves are more likely to reverse or stall.
Combined Chop Intensity:
chopIntensity = (adx_chop × 0.25) + (chop_idx_score × 0.25) +
(range_compression_score × 0.20) + (channel_chop × 0.15) +
(volume_chop × i_volumeChopWeight × 0.15)
Regime Classifications:
Based on chop intensity and component analysis:
• Strong Trend (0-20%): ADX >30, clear directional momentum, trade aggressively
• Trending (20-35%): ADX >20, moderate directional bias, trade normally
• Transitioning (35-50%): Mixed signals, regime change possible, reduce size
• Mid-Range (50-60%): Price trapped in channel center, avoid new positions
• Ranging (60-70%): Low ADX, price oscillating within bounds, fade extremes only
• Compression (70-80%): Volatility squeeze, expansion imminent, wait for breakout
• Strong Chop (80-100%): Multiple chop factors aligned, avoid trading entirely
Signal Suppression:
When chop intensity exceeds the configurable threshold (default 80%), signals are suppressed entirely. The dashboard displays "⚠️ CHOP ZONE" with the current regime classification.
Chop Box Visualization:
When chop is detected, AMWT draws a semi-transparent box on the chart showing the chop zone. This visual reminder helps traders avoid entering positions during unfavorable conditions.
💧 LIQUIDITY ANCHORING SYSTEM
The Liquidity Concept:
Markets move from liquidity pool to liquidity pool. Stop losses cluster at predictable locations—below swing lows (buy stops become sell orders when triggered) and above swing highs (sell stops become buy orders when triggered). Institutions know where these clusters are and often engineer moves to trigger them before reversing.
AMWT identifies and tracks these liquidity events, using them as anchors for signal confidence.
Liquidity Event Types:
Type 1: Volume Spikes
Definition: Volume > SMA(volume, 20) × i_volThreshold (default 2.8x)
Interpretation: Sudden volume surge indicates institutional activity
• Near swing low + reversal: Likely accumulation
• Near swing high + reversal: Likely distribution
• With continuation: Institutional conviction in direction
Type 2: Stop Runs (Liquidity Sweeps)
Definition: Price briefly exceeds swing high/low then reverses within N bars
Detection:
• Price breaks above recent swing high (triggering buy stops)
• Then closes back below that high within 3 bars
• Signal: Bullish stop run complete, reversal likely
Or inverse for bearish:
• Price breaks below recent swing low (triggering sell stops)
• Then closes back above that low within 3 bars
• Signal: Bearish stop run complete, reversal likely
Type 3: Absorption Events
Definition: High volume with small candle body
Detection:
• Volume > 2x average
• Candle body < 30% of candle range
• Interpretation: Large orders being filled without moving price
• Implication: Accumulation (at lows) or distribution (at highs)
Type 4: BSL/SSL Pools (Buy-Side/Sell-Side Liquidity)
BSL (Buy-Side Liquidity):
• Cluster of swing highs within ATR proximity
• Stop losses from shorts sit above these highs
• Breaking BSL triggers short covering (fuel for rally)
SSL (Sell-Side Liquidity):
• Cluster of swing lows within ATR proximity
• Stop losses from longs sit below these lows
• Breaking SSL triggers long liquidation (fuel for decline)
Liquidity Pool Mapping:
AMWT continuously scans for and maps liquidity pools:
// Detect swing highs/lows using pivot function
swing_high = ta.pivothigh(high, 5, 5)
swing_low = ta.pivotlow(low, 5, 5)
// Track recent swing points
if not na(swing_high)
bsl_levels.push(swing_high)
if not na(swing_low)
ssl_levels.push(swing_low)
// Display on chart with labels
Confluence Scoring Integration:
When signals fire near identified liquidity events, confluence scoring increases:
• Signal near volume spike: +10% confidence
• Signal after liquidity sweep: +15% confidence
• Signal at BSL/SSL pool: +10% confidence
• Signal aligned with absorption zone: +10% confidence
Why Liquidity Anchoring Matters:
Signals "in a vacuum" have lower probability than signals anchored to institutional activity. A long signal after a liquidity sweep below swing lows has trapped shorts providing fuel. A long signal in the middle of nowhere has no such catalyst.
📊 SIGNAL GRADING SYSTEM
The Quality Problem:
Not all signals are created equal. A signal with 6/6 factors aligned is fundamentally different from a signal with 3/6 factors aligned. Traditional indicators treat them the same. AMWT grades every signal based on confluence.
Confluence Components (100 points total):
1. Bandit Consensus Strength (25 points)
consensus_str = weighted average of agent confidences
score = consensus_str × 25
Example:
Trend Agent: +1 signal, 0.80 confidence, 0.35 weight
Reversion Agent: 0 signal, 0.50 confidence, 0.25 weight
Structure Agent: +1 signal, 0.75 confidence, 0.40 weight
Weighted consensus = (0.80×0.35 + 0×0.25 + 0.75×0.40) / (0.35 + 0.40) = 0.77
Score = 0.77 × 25 = 19.25 points
2. HMM State Confidence (15 points)
score = hmm_confidence × 15
Example:
HMM reports 82% probability of IMPULSE_UP
Score = 0.82 × 15 = 12.3 points
3. Session Quality (15 points)
Session quality varies by time:
• London/NY Overlap: 1.0 (15 points)
• New York Session: 0.95 (14.25 points)
• London Session: 0.70 (10.5 points)
• Asian Session: 0.40 (6 points)
• Off-Hours: 0.30 (4.5 points)
• Weekend: 0.10 (1.5 points)
4. Energy/Participation (10 points)
energy = (realized_vol / avg_vol) × 0.4 + (range / ATR) × 0.35 + (volume / avg_volume) × 0.25
score = min(energy, 1.0) × 10
5. Volume Confirmation (10 points)
if volume > SMA(volume, 20) × 1.5:
score = 10
else if volume > SMA(volume, 20):
score = 5
else:
score = 0
6. Structure Alignment (10 points)
For long signals:
• Bullish structure (HH + HL): 10 points
• Higher low only: 6 points
• Neutral structure: 3 points
• Bearish structure: 0 points
Inverse for short signals
7. Trend Alignment (10 points)
For long signals:
• Price > EMA21 > EMA50: 10 points
• Price > EMA21: 6 points
• Neutral: 3 points
• Against trend: 0 points
8. Entry Trigger Quality (5 points)
• Strong trigger (multiple confirmations): 5 points
• Moderate trigger (single confirmation): 3 points
• Weak trigger (marginal): 1 point
Grade Scale:
Total Score → Grade
85-100 → A+ (Exceptional—all factors aligned)
70-84 → A (Strong—high probability)
55-69 → B (Acceptable—proceed with caution)
Below 55 → C (Marginal—filtered by default)
Grade-Based Signal Brightness:
Signal arrows on the chart have transparency based on grade:
• A+: Full brightness (alpha = 0)
• A: Slight fade (alpha = 15)
• B: Moderate fade (alpha = 35)
• C: Significant fade (alpha = 55)
This visual hierarchy helps traders instantly identify signal quality.
Minimum Grade Filter:
Configurable filter (default: C) sets the minimum grade for signal display:
• Set to "A" for only highest-quality signals
• Set to "B" for moderate selectivity
• Set to "C" for all signals (maximum quantity)
🕐 SESSION INTELLIGENCE
Why Sessions Matter:
Markets behave differently at different times. The London open is fundamentally different from the Asian lunch hour. AMWT incorporates session-aware logic to optimize signal quality.
Session Definitions:
Asian Session (18:00-03:00 ET)
• Characteristics: Lower volatility, range-bound tendency, fewer institutional participants
• Quality Score: 0.40 (40% of peak quality)
• Strategy Implications: Fade extremes, expect ranges, smaller position sizes
• Best For: Mean-reversion setups, accumulation/distribution identification
London Session (03:00-12:00 ET)
• Characteristics: European institutional activity, volatility pickup, trend initiation
• Quality Score: 0.70 (70% of peak quality)
• Strategy Implications: Watch for trend development, breakouts more reliable
• Best For: Initial trend identification, structure breaks
New York Session (08:00-17:00 ET)
• Characteristics: Highest liquidity, US institutional activity, major moves
• Quality Score: 0.95 (95% of peak quality)
• Strategy Implications: Best environment for directional trades
• Best For: Trend continuation, momentum plays
London/NY Overlap (08:00-12:00 ET)
• Characteristics: Peak liquidity, both European and US participants active
• Quality Score: 1.0 (100%—maximum quality)
• Strategy Implications: Highest probability for successful breakouts and trends
• Best For: All signal types—this is prime time
Off-Hours
• Characteristics: Thin liquidity, erratic price action, gaps possible
• Quality Score: 0.30 (30% of peak quality)
• Strategy Implications: Avoid new positions, wider stops if holding
• Best For: Waiting
Smart Weekend Detection:
AMWT properly handles the Sunday evening futures open:
// Traditional (broken):
isWeekend = dayofweek == saturday OR dayofweek == sunday
// AMWT (correct):
anySessionActive = not na(asianTime) or not na(londonTime) or not na(nyTime)
isWeekend = calendarWeekend AND NOT anySessionActive
This ensures Sunday 6pm ET (when futures open) correctly shows "Asian Session" rather than "Weekend."
Session Transition Boosts:
Certain session transitions create trading opportunities:
• Asian → London transition: +15% confidence boost (volatility expansion likely)
• London → Overlap transition: +20% confidence boost (peak liquidity approaching)
• Overlap → NY-only transition: -10% confidence adjustment (liquidity declining)
• Any → Off-Hours transition: Signal suppression recommended
📈 TRADE MANAGEMENT SYSTEM
The Signal Spam Problem:
Many indicators generate signal after signal, creating confusion and overtrading. AMWT implements a complete trade lifecycle management system that prevents signal spam and tracks performance.
Trade Lock Mechanism:
Once a signal fires, the system enters a "trade lock" state:
Trade Lock Duration: Configurable (default 30 bars)
Early Exit Conditions:
• TP3 hit (full target reached)
• Stop Loss hit (trade failed)
• Lock expiration (time-based exit)
During lock:
• No new signals of same type displayed
• Opposite signals can override (reversal)
• Trade status tracked in dashboard
Target Levels:
Each signal generates three profit targets based on ATR:
TP1 (Conservative Target)
• Default: 1.0 × ATR
• Purpose: Quick partial profit, reduce risk
• Action: Take 30-40% off position, move stop to breakeven
TP2 (Standard Target)
• Default: 2.5 × ATR
• Purpose: Main profit target
• Action: Take 40-50% off position, trail stop
TP3 (Extended Target)
• Default: 5.0 × ATR
• Purpose: Runner target for trend days
• Action: Close remaining position or continue trailing
Stop Loss:
• Default: 1.9 × ATR from entry
• Purpose: Define maximum risk
• Placement: Below recent swing low (longs) or above recent swing high (shorts)
Invalidation Level:
Beyond stop loss, AMWT calculates an "invalidation" level where the wave hypothesis dies:
invalidation = entry - (ATR × INVALIDATION_MULT × 1.5)
If price reaches invalidation, the current market interpretation is wrong—not just the trade.
Visual Trade Management:
During active trades, AMWT displays:
• Entry arrow with grade label (▲A+, ▼B, etc.)
• TP1, TP2, TP3 horizontal lines in green
• Stop Loss line in red
• Invalidation line in orange (dashed)
• Progress indicator in dashboard
Persistent Execution Markers:
When targets or stops are hit, permanent markers appear:
• TP hit: Green dot with "TP1"/"TP2"/"TP3" label
• SL hit: Red dot with "SL" label
These persist on the chart for review and statistics.
💰 PERFORMANCE TRACKING & STATISTICS
Tracked Metrics:
• Total Trades: Count of all signals that entered trade lock
• Winning Trades: Signals where at least TP1 was reached before SL
• Losing Trades: Signals where SL was hit before any TP
• Win Rate: Winning / Total × 100%
• Total R Profit: Sum of R-multiples from winning trades
• Total R Loss: Sum of R-multiples from losing trades
• Net R: Total R Profit - Total R Loss
Currency Conversion System:
AMWT can display P&L in multiple formats:
R-Multiple (Default)
• Shows risk-normalized returns
• "Net P&L: +4.2R | 78 trades" means 4.2 times initial risk gained over 78 trades
• Best for comparing across different position sizes
Currency Conversion (USD/EUR/GBP/JPY/INR)
• Converts R-multiples to currency based on:
- Dollar Risk Per Trade (user input)
- Tick Value (user input)
- Selected currency
Example Configuration:
Dollar Risk Per Trade: $100
Display Currency: USD
If Net R = +4.2R
Display: Net P&L: +$420.00 | 78 trades
Ticks
• For futures traders who think in ticks
• Converts based on tick value input
Statistics Reset:
Two reset methods:
1. Toggle Reset
• Turn "Reset Statistics" toggle ON then OFF
• Clears all statistics immediately
2. Date-Based Reset
• Set "Reset After Date" (YYYY-MM-DD format)
• Only trades after this date are counted
• Useful for isolating recent performance
🎨 VISUAL FEATURES
Macro Channel:
Dynamic regression-based channel showing market boundaries:
• Upper/lower bounds calculated from swing pivot linear regression
• Adapts to current market structure
• Shows overall trend direction and potential reversal zones
Chop Boxes:
Semi-transparent overlay during high-chop periods:
• Purple/orange coloring indicates dangerous conditions
• Visual reminder to avoid new positions
Confluence Heat Zones:
Background shading indicating setup quality:
• Darker shading = higher confluence
• Lighter shading = lower confluence
• Helps identify optimal entry timing
EMA Ribbon:
Trend visualization via moving average fill:
• EMA 8/21/50 with gradient fill between
• Green fill when bullish aligned
• Red fill when bearish aligned
• Gray when neutral
Absorption Zone Boxes:
Marks potential accumulation/distribution areas:
• High volume + small body = absorption
• Boxes drawn at these levels
• Often act as support/resistance
Liquidity Pool Lines:
BSL/SSL levels with labels:
• Dashed lines at liquidity clusters
• "BSL" label above swing high clusters
• "SSL" label below swing low clusters
Six Professional Themes:
• Quantum: Deep purples and cyans (default)
• Cyberpunk: Neon pinks and blues
• Professional: Muted grays and greens
• Ocean: Blues and teals
• Matrix: Greens and blacks
• Ember: Oranges and reds
🎓 PROFESSIONAL USAGE PROTOCOL
Phase 1: Learning the System (Week 1)
Goal: Understand AMWT concepts and dashboard interpretation
Setup:
• Signal Mode: Balanced
• Display: All features enabled
• Grade Filter: C (see all signals)
Actions:
• Paper trade ONLY—no real money
• Observe HMM state transitions throughout the day
• Note when agents agree vs disagree
• Watch chop detection engage and disengage
• Track which grades produce winners vs losers
Key Learning Questions:
• How often do A+ signals win vs B signals? (Should see clear difference)
• Which agent tends to be right in current market? (Check dashboard)
• When does chop detection save you from bad trades?
• How do signals near liquidity events perform vs signals in vacuum?
Phase 2: Parameter Optimization (Week 2)
Goal: Tune system to your instrument and timeframe
Signal Mode Testing:
• Run 5 days on Aggressive mode (more signals)
• Run 5 days on Conservative mode (fewer signals)
• Compare: Which produces better risk-adjusted returns?
Grade Filter Testing:
• Track A+ only for 20 signals
• Track A and above for 20 signals
• Track B and above for 20 signals
• Compare win rates and expectancy
Chop Threshold Testing:
• Default (80%): Standard filtering
• Try 70%: More aggressive filtering
• Try 90%: Less filtering
• Which produces best results for your instrument?
Phase 3: Strategy Development (Weeks 3-4)
Goal: Develop personal trading rules based on system signals
Position Sizing by Grade:
• A+ grade: 100% position size
• A grade: 75% position size
• B grade: 50% position size
• C grade: 25% position size (or skip)
Session-Based Rules:
• London/NY Overlap: Take all A/A+ signals
• NY Session: Take all A+ signals, selective on A
• Asian Session: Only A+ signals with extra confirmation
• Off-Hours: No new positions
Chop Zone Rules:
• Chop >70%: Reduce position size 50%
• Chop >80%: No new positions
• Chop <50%: Full position size allowed
Phase 4: Live Micro-Sizing (Month 2)
Goal: Validate paper trading results with minimal risk
Setup:
• 10-20% of intended full position size
• Take ONLY A+ signals initially
• Follow trade management religiously
Tracking:
• Log every trade: Entry, Exit, Grade, HMM State, Chop Level, Agent Consensus
• Calculate: Win rate by grade, by session, by chop level
• Compare to paper trading (should be within 15%)
Red Flags:
• Win rate diverges significantly from paper trading: Execution issues
• Consistent losses during certain sessions: Adjust session rules
• Losses cluster when specific agent dominates: Review that agent's logic
Phase 5: Scaling Up (Months 3-6)
Goal: Gradually increase to full position size
Progression:
• Month 3: 25-40% size (if micro-sizing profitable)
• Month 4: 40-60% size
• Month 5: 60-80% size
• Month 6: 80-100% size
Scale-Up Requirements:
• Minimum 30 trades at current size
• Win rate ≥50%
• Net R positive
• No revenge trading incidents
• Emotional control maintained
💡 DEVELOPMENT INSIGHTS
Why HMM Over Simple Indicators:
Early versions used standard indicators (RSI >70 = overbought, etc.). Win rates hovered at 52-55%. The problem: indicators don't capture state. RSI can stay "overbought" for weeks in a strong trend.
The insight: markets exist in states, and state persistence matters more than indicator levels. Implementing HMM with state transition probabilities increased signal quality significantly. The system now knows not just "RSI is high" but "we're in IMPULSE_UP state with 70% probability of staying in IMPULSE_UP."
The Multi-Agent Evolution:
Original version used a single analytical methodology—trend-following. Performance was inconsistent: great in trends, destroyed in ranges. Added mean-reversion agent: now it was inconsistent the other way.
The breakthrough: use multiple agents and let the system learn which works . Thompson Sampling wasn't the first attempt—tried simple averaging, voting, even hard-coded regime switching. Thompson Sampling won because it's mathematically optimal and automatically adapts without manual regime detection.
Chop Detection Revelation:
Chop detection was added almost as an afterthought. "Let's filter out obviously bad conditions." Testing revealed it was the most impactful single feature. Filtering chop zones reduced losing trades by 35% while only reducing total signals by 20%. The insight: avoiding bad trades matters more than finding good ones.
Liquidity Anchoring Discovery:
Watched hundreds of trades. Noticed pattern: signals that fired after liquidity events (stop runs, volume spikes) had significantly higher win rates than signals in quiet markets. Implemented liquidity detection and anchoring. Win rate on liquidity-anchored signals: 68% vs 52% on non-anchored signals.
The Grade System Impact:
Early system had binary signals (fire or don't fire). Adding grading transformed it. Traders could finally match position size to signal quality. A+ signals deserved full size; C signals deserved caution. Just implementing grade-based sizing improved portfolio Sharpe ratio by 0.3.
🚨 LIMITATIONS & CRITICAL ASSUMPTIONS
What AMWT Is NOT:
• NOT a Holy Grail : No system wins every trade. AMWT improves probability, not certainty.
• NOT Fully Automated : AMWT provides signals and analysis; execution requires human judgment.
• NOT News-Proof : Exogenous shocks (FOMC surprises, geopolitical events) invalidate all technical analysis.
• NOT for Scalping : HMM state estimation needs time to develop. Sub-minute timeframes are not appropriate.
Core Assumptions:
1. Markets Have States : Assumes markets transition between identifiable regimes. Violation: Random walk markets with no regime structure.
2. States Are Inferable : Assumes observable indicators reveal hidden states. Violation: Market manipulation creating false signals.
3. History Informs Future : Assumes past agent performance predicts future performance. Violation: Regime changes that invalidate historical patterns.
4. Liquidity Events Matter : Assumes institutional activity creates predictable patterns. Violation: Markets with no institutional participation.
Performs Best On:
• Liquid Futures : ES, NQ, MNQ, MES, CL, GC
• Major Forex Pairs : EUR/USD, GBP/USD, USD/JPY
• Large-Cap Stocks : AAPL, MSFT, TSLA, NVDA (>$5B market cap)
• Liquid Crypto : BTC, ETH on major exchanges
Performs Poorly On:
• Illiquid Instruments : Low volume stocks, exotic pairs
• Very Low Timeframes : Sub-5-minute charts (noise overwhelms signal)
• Binary Event Days : Earnings, FDA approvals, court rulings
• Manipulated Markets : Penny stocks, low-cap altcoins
Known Weaknesses:
• Warmup Period : HMM needs ~50 bars to initialize properly. Early signals may be unreliable.
• Regime Change Lag : Thompson Sampling adapts over time, not instantly. Sudden regime changes may cause short-term underperformance.
• Complexity : More parameters than simple indicators. Requires understanding to use effectively.
⚠️ RISK DISCLOSURE
Trading futures, stocks, options, forex, and cryptocurrencies involves substantial risk of loss and is not suitable for all investors. Adaptive Market Wave Theory, while based on rigorous mathematical frameworks including Hidden Markov Models and multi-armed bandit algorithms, does not guarantee profits and can result in significant losses.
AMWT's methodologies—HMM state estimation, Thompson Sampling agent selection, and confluence-based grading—have theoretical foundations but past performance is not indicative of future results.
Hidden Markov Model assumptions may not hold during:
• Major news events disrupting normal market behavior
• Flash crashes or circuit breaker events
• Low liquidity periods with erratic price action
• Algorithmic manipulation or spoofing
Multi-agent consensus assumes independent analytical perspectives provide edge. Market conditions change. Edges that existed historically can diminish or disappear.
Users must independently validate system performance on their specific instruments, timeframes, and broker execution environment. Paper trade extensively before risking capital. Start with micro position sizing.
Never risk more than you can afford to lose completely. Use proper position sizing. Implement stop losses without exception.
By using this indicator, you acknowledge these risks and accept full responsibility for all trading decisions and outcomes.
"Elliott Wave was a first-order approximation of market phase behavior. AMWT is the second—probabilistic, adaptive, and accountable."
Initial Public Release
Core Engine:
• True Hidden Markov Model with online Baum-Welch learning
• Viterbi algorithm for optimal state sequence decoding
• 6-state market regime classification
Agent System:
• 3-Bandit consensus (Trend, Reversion, Structure)
• Thompson Sampling with true Beta distribution sampling
• Adaptive weight learning based on performance
Signal Generation:
• Quality-based confluence grading (A+/A/B/C)
• Four signal modes (Aggressive/Balanced/Conservative/Institutional)
• Grade-based visual brightness
Chop Detection:
• 5-factor analysis (ADX, Choppiness Index, Range Compression, Channel Position, Volume)
• 7 regime classifications
• Configurable signal suppression threshold
Liquidity:
• Volume spike detection
• Stop run (liquidity sweep) identification
• BSL/SSL pool mapping
• Absorption zone detection
Trade Management:
• Trade lock with configurable duration
• TP1/TP2/TP3 targets
• ATR-based stop loss
• Persistent execution markers
Session Intelligence:
• Asian/London/NY/Overlap detection
• Smart weekend handling (Sunday futures open)
• Session quality scoring
Performance:
• Statistics tracking with reset functionality
• 7 currency display modes
• Win rate and Net R calculation
Visuals:
• Macro channel with linear regression
• Chop boxes
• EMA ribbon
• Liquidity pool lines
• 6 professional themes
Dashboards:
• Main Dashboard: Market State, Consensus, Trade Status, Statistics
📋 AMWT vs AMWT-PRO:
This version includes all core AMWT functionality:
✓ Full Hidden Markov Model state estimation
✓ 3-Bandit Thompson Sampling consensus system
✓ Complete 5-factor chop detection engine
✓ All four signal modes
✓ Full trade management with TP/SL tracking
✓ Main dashboard with complete statistics
✓ All visual features (channels, zones, pools)
✓ Identical signal generation to PRO
✓ Six professional themes
✓ Full alert system
The PRO version adds the AMWT Advisor panel—a secondary dashboard providing:
• Real-time Market Pulse situation assessment
• Agent Matrix visualization (individual agent votes)
• Structure analysis breakdown
• "Watch For" upcoming setups
• Action Command coaching
Both versions generate identical signals . The Advisor provides additional guidance for interpreting those signals.
Taking you to school. - Dskyz, Trade with probability. Trade with consensus. Trade with AMWT.
ORB Fusion🎯 CORE INNOVATION: INSTITUTIONAL ORB FRAMEWORK WITH FAILED BREAKOUT INTELLIGENCE
ORB Fusion represents a complete institutional-grade Opening Range Breakout system combining classic Market Profile concepts (Initial Balance, day type classification) with modern algorithmic breakout detection, failed breakout reversal logic, and comprehensive statistical tracking. Rather than simply drawing lines at opening range extremes, this system implements the full trading methodology used by professional floor traders and market makers—including the critical concept that failed breakouts are often higher-probability setups than successful breakouts .
The Opening Range Hypothesis:
The first 30-60 minutes of trading establishes the day's value area —the price range where the majority of participants agree on fair value. This range is formed during peak information flow (overnight news digestion, gap reactions, early institutional positioning). Breakouts from this range signal directional conviction; failures to hold breakouts signal trapped participants and create exploitable reversals.
Why Opening Range Matters:
1. Information Aggregation : Opening range reflects overnight news, pre-market sentiment, and early institutional orders. It's the market's initial "consensus" on value.
2. Liquidity Concentration : Stop losses cluster just outside opening range. Breakouts trigger these stops, creating momentum. Failed breakouts trap traders, forcing reversals.
3. Statistical Persistence : Markets exhibit range expansion tendency —when price accepts above/below opening range with volume, it often extends 1.0-2.0x the opening range size before mean reversion.
4. Institutional Behavior : Large players (market makers, institutions) use opening range as reference for the day's trading plan. They fade extremes in rotation days and follow breakouts in trend days.
Historical Context:
Opening Range Breakout methodology originated in commodity futures pits (1970s-80s) where floor traders noticed consistent patterns: the first 30-60 minutes established a "fair value zone," and directional moves occurred when this zone was violated with conviction. J. Peter Steidlmayer formalized this observation in Market Profile theory, introducing the "Initial Balance" concept—the first hour (two 30-minute periods) defining market structure.
📊 OPENING RANGE CONSTRUCTION
Four ORB Timeframe Options:
1. 5-Minute ORB (0930-0935 ET):
Captures immediate market direction during "opening drive"—the explosive first few minutes when overnight orders hit the tape.
Use Case:
• Scalping strategies
• High-frequency breakout trading
• Extremely liquid instruments (ES, NQ, SPY)
Characteristics:
• Very tight range (often 0.2-0.5% of price)
• Early breakouts common (7 of 10 days break within first hour)
• Higher false breakout rate (50-60%)
• Requires sub-minute chart monitoring
Psychology: Captures panic buyers/sellers reacting to overnight news. Range is small because sample size is minimal—only 5 minutes of price discovery. Early breakouts often fail because they're driven by retail FOMO rather than institutional conviction.
2. 15-Minute ORB (0930-0945 ET):
Balances responsiveness with statistical validity. Captures opening drive plus initial reaction to that drive.
Use Case:
• Day trading strategies
• Balanced scalping/swing hybrid
• Most liquid instruments
Characteristics:
• Moderate range (0.4-0.8% of price typically)
• Breakout rate ~60% of days
• False breakout rate ~40-45%
• Good balance of opportunity and reliability
Psychology: Includes opening panic AND the first retest/consolidation. Sophisticated traders (institutions, algos) start expressing directional bias. This is the "Goldilocks" timeframe—not too reactive, not too slow.
3. 30-Minute ORB (0930-1000 ET):
Classic ORB timeframe. Default for most professional implementations.
Use Case:
• Standard intraday trading
• Position sizing for full-day trades
• All liquid instruments (equities, indices, futures)
Characteristics:
• Substantial range (0.6-1.2% of price)
• Breakout rate ~55% of days
• False breakout rate ~35-40%
• Statistical sweet spot for extensions
Psychology: Full opening auction + first institutional repositioning complete. By 10:00 AM ET, headlines are digested, early stops are hit, and "real" directional players reveal themselves. This is when institutional programs typically finish their opening positioning.
Statistical Advantage: 30-minute ORB shows highest correlation with daily range. When price breaks and holds outside 30m ORB, probability of reaching 1.0x extension (doubling the opening range) exceeds 60% historically.
4. 60-Minute ORB (0930-1030 ET) - Initial Balance:
Steidlmayer's "Initial Balance"—the foundation of Market Profile theory.
Use Case:
• Swing trading entries
• Day type classification
• Low-frequency institutional setups
Characteristics:
• Wide range (0.8-1.5% of price)
• Breakout rate ~45% of days
• False breakout rate ~25-30% (lowest)
• Best for trend day identification
Psychology: Full first hour captures A-period (0930-1000) and B-period (1000-1030). By 10:30 AM ET, all early positioning is complete. Market has "voted" on value. Subsequent price action confirms (trend day) or rejects (rotation day) this value assessment.
Initial Balance Theory:
IB represents the market's accepted value area . When price extends significantly beyond IB (>1.5x IB range), it signals a Trend Day —strong directional conviction. When price remains within 1.0x IB, it signals a Rotation Day —mean reversion environment. This classification completely changes trading strategy.
🔬 LTF PRECISION TECHNOLOGY
The Chart Timeframe Problem:
Traditional ORB indicators calculate range using the chart's current timeframe. This creates critical inaccuracies:
Example:
• You're on a 5-minute chart
• ORB period is 30 minutes (0930-1000 ET)
• Indicator sees only 6 bars (30min ÷ 5min/bar = 6 bars)
• If any 5-minute bar has extreme wick, entire ORB is distorted
The Problem Amplifies:
• On 15-minute chart with 30-minute ORB: Only 2 bars sampled
• On 30-minute chart with 30-minute ORB: Only 1 bar sampled
• Opening spike or single large wick defines entire range (invalid)
Solution: Lower Timeframe (LTF) Precision:
ORB Fusion uses `request.security_lower_tf()` to sample 1-minute bars regardless of chart timeframe:
```
For 30-minute ORB on 15-minute chart:
- Traditional method: Uses 2 bars (15min × 2 = 30min)
- LTF Precision: Requests thirty 1-minute bars, calculates true high/low
```
Why This Matters:
Scenario: ES futures, 15-minute chart, 30-minute ORB
• Traditional ORB: High = 5850.00, Low = 5842.00 (range = 8 points)
• LTF Precision ORB: High = 5848.50, Low = 5843.25 (range = 5.25 points)
Difference: 2.75 points distortion from single 15-minute wick hitting 5850.00 at 9:31 AM then immediately reversing. LTF precision filters this out by seeing it was a fleeting wick, not a sustained high.
Impact on Extensions:
With inflated range (8 points vs 5.25 points):
• 1.5x extension projects +12 points instead of +7.875 points
• Difference: 4.125 points (nearly $200 per ES contract)
• Breakout signals trigger late; extension targets unreachable
Implementation:
```pinescript
getLtfHighLow() =>
float ha = request.security_lower_tf(syminfo.tickerid, "1", high)
float la = request.security_lower_tf(syminfo.tickerid, "1", low)
```
Function returns arrays of 1-minute high/low values, then finds true maximum and minimum across all samples.
When LTF Precision Activates:
Only when chart timeframe exceeds ORB session window:
• 5-minute chart + 30-minute ORB: LTF used (chart TF > session bars needed)
• 1-minute chart + 30-minute ORB: LTF not needed (direct sampling sufficient)
Recommendation: Always enable LTF Precision unless you're on 1-minute charts. The computational overhead is negligible, and accuracy improvement is substantial.
⚖️ INITIAL BALANCE (IB) FRAMEWORK
Steidlmayer's Market Profile Innovation:
J. Peter Steidlmayer developed Market Profile in the 1980s for the Chicago Board of Trade. His key insight: market structure is best understood through time-at-price (value area) rather than just price-over-time (traditional charts).
Initial Balance Definition:
IB is the price range established during the first hour of trading, subdivided into:
• A-Period : First 30 minutes (0930-1000 ET for US equities)
• B-Period : Second 30 minutes (1000-1030 ET)
A-Period vs B-Period Comparison:
The relationship between A and B periods forecasts the day:
B-Period Expansion (Bullish):
• B-period high > A-period high
• B-period low ≥ A-period low
• Interpretation: Buyers stepping in after opening assessed
• Implication: Bullish continuation likely
• Strategy: Buy pullbacks to A-period high (now support)
B-Period Expansion (Bearish):
• B-period low < A-period low
• B-period high ≤ A-period high
• Interpretation: Sellers stepping in after opening assessed
• Implication: Bearish continuation likely
• Strategy: Sell rallies to A-period low (now resistance)
B-Period Contraction:
• B-period stays within A-period range
• Interpretation: Market indecisive, digesting A-period information
• Implication: Rotation day likely, stay range-bound
• Strategy: Fade extremes, sell high/buy low within IB
IB Extensions:
Professional traders use IB as a ruler to project price targets:
Extension Levels:
• 0.5x IB : Initial probe outside value (minor target)
• 1.0x IB : Full extension (major target for normal days)
• 1.5x IB : Trend day threshold (classifies as trending)
• 2.0x IB : Strong trend day (rare, ~10-15% of days)
Calculation:
```
IB Range = IB High - IB Low
Bull Extension 1.0x = IB High + (IB Range × 1.0)
Bear Extension 1.0x = IB Low - (IB Range × 1.0)
```
Example:
ES futures:
• IB High: 5850.00
• IB Low: 5842.00
• IB Range: 8.00 points
Extensions:
• 1.0x Bull Target: 5850 + 8 = 5858.00
• 1.5x Bull Target: 5850 + 12 = 5862.00
• 2.0x Bull Target: 5850 + 16 = 5866.00
If price reaches 5862.00 (1.5x), day is classified as Trend Day —strategy shifts from mean reversion to trend following.
📈 DAY TYPE CLASSIFICATION SYSTEM
Four Day Types (Market Profile Framework):
1. TREND DAY:
Definition: Price extends ≥1.5x IB range in one direction and stays there.
Characteristics:
• Opens and never returns to IB
• Persistent directional movement
• Volume increases as day progresses (conviction building)
• News-driven or strong institutional flow
Frequency: ~20-25% of trading days
Trading Strategy:
• DO: Follow the trend, trail stops, let winners run
• DON'T: Fade extremes, take early profits
• Key: Add to position on pullbacks to previous extension level
• Risk: Getting chopped in false trend (see Failed Breakout section)
Example: FOMC decision, payroll report, earnings surprise—anything creating one-sided conviction.
2. NORMAL DAY:
Definition: Price extends 0.5-1.5x IB, tests both sides, returns to IB.
Characteristics:
• Two-sided trading
• Extensions occur but don't persist
• Volume balanced throughout day
• Most common day type
Frequency: ~45-50% of trading days
Trading Strategy:
• DO: Take profits at extension levels, expect reversals
• DON'T: Hold for massive moves
• Key: Treat each extension as a profit-taking opportunity
• Risk: Holding too long when momentum shifts
Example: Typical day with no major catalysts—market balancing supply and demand.
3. ROTATION DAY:
Definition: Price stays within IB all day, rotating between high and low.
Characteristics:
• Never accepts outside IB
• Multiple tests of IB high/low
• Decreasing volume (no conviction)
• Classic range-bound action
Frequency: ~25-30% of trading days
Trading Strategy:
• DO: Fade extremes (sell IB high, buy IB low)
• DON'T: Chase breakouts
• Key: Enter at extremes with tight stops just outside IB
• Risk: Breakout finally occurs after multiple failures
Example: [/b> Pre-holiday trading, summer doldrums, consolidation after big move.
4. DEVELOPING:
Definition: Day type not yet determined (early in session).
Usage: Classification before 12:00 PM ET when IB extension pattern unclear.
ORB Fusion's Classification Algorithm:
```pinescript
if close > ibHigh:
ibExtension = (close - ibHigh) / ibRange
direction = "BULLISH"
else if close < ibLow:
ibExtension = (ibLow - close) / ibRange
direction = "BEARISH"
if ibExtension >= 1.5:
dayType = "TREND DAY"
else if ibExtension >= 0.5:
dayType = "NORMAL DAY"
else if close within IB:
dayType = "ROTATION DAY"
```
Why Classification Matters:
Same setup (bullish ORB breakout) has opposite implications:
• Trend Day : Hold for 2.0x extension, trail stops aggressively
• Normal Day : Take profits at 1.0x extension, watch for reversal
• Rotation Day : Fade the breakout immediately (likely false)
Knowing day type prevents catastrophic errors like fading a trend day or holding through rotation.
🚀 BREAKOUT DETECTION & CONFIRMATION
Three Confirmation Methods:
1. Close Beyond Level (Recommended):
Logic: Candle must close above ORB high (bull) or below ORB low (bear).
Why:
• Filters out wicks (temporary liquidity grabs)
• Ensures sustained acceptance above/below range
• Reduces false breakout rate by ~20-30%
Example:
• ORB High: 5850.00
• Bar high touches 5850.50 (wick above)
• Bar closes at 5848.00 (inside range)
• Result: NO breakout signal
vs.
• Bar high touches 5850.50
• Bar closes at 5851.00 (outside range)
• Result: BREAKOUT signal confirmed
Trade-off: Slightly delayed entry (wait for close) but much higher reliability.
2. Wick Beyond Level:
Logic: [/b> Any touch of ORB high/low triggers breakout.
Why:
• Earliest possible entry
• Captures aggressive momentum moves
Risk:
• High false breakout rate (60-70%)
• Stop runs trigger signals
• Requires very tight stops (difficult to manage)
Use Case: Scalping with 1-2 point profit targets where any penetration = trade.
3. Body Beyond Level:
Logic: [/b> Candle body (close vs open) must be entirely outside range.
Why:
• Strictest confirmation
• Ensures directional conviction (not just momentum)
• Lowest false breakout rate
Example: Trade-off: [/b> Very conservative—misses some valid breakouts but rarely triggers on false ones.
Volume Confirmation Layer:
All confirmation methods can require volume validation:
Volume Multiplier Logic: Rationale: [/b> True breakouts are driven by institutional activity (large size). Volume spike confirms real conviction vs. stop-run manipulation.
Statistical Impact: [/b>
• Breakouts with volume confirmation: ~65% success rate
• Breakouts without volume: ~45% success rate
• Difference: 20 percentage points edge
Implementation Note: [/b>
Volume confirmation adds complexity—you'll miss breakouts that work but lack volume. However, when targeting 1.5x+ extensions (ambitious goals), volume confirmation becomes critical because those moves require sustained institutional participation.
Recommended Settings by Strategy: [/b>
Scalping (1-2 point targets): [/b>
• Method: Close
• Volume: OFF
• Rationale: Quick in/out doesn't need perfection
Intraday Swing (5-10 point targets): [/b>
• Method: Close
• Volume: ON (1.5x multiplier)
• Rationale: Balance reliability and opportunity
Position Trading (full-day holds): [/b>
• Method: Body
• Volume: ON (2.0x multiplier)
• Rationale: Must be certain—large stops require high win rate
🔥 FAILED BREAKOUT SYSTEM
The Core Insight: [/b>
Failed breakouts are often more profitable [/b> than successful breakouts because they create trapped traders with predictable behavior.
Failed Breakout Definition: [/b>
A breakout that:
1. Initially penetrates ORB level with confirmation
2. Attracts participants (volume spike, momentum)
3. Fails to extend (stalls or immediately reverses)
4. Returns inside ORB range within N bars
Psychology of Failure: [/b>
When breakout fails:
• Breakout buyers are trapped [/b>: Bought at ORB high, now underwater
• Early longs reduce: Take profit, fearful of reversal
• Shorts smell blood: See failed breakout as reversal signal
• Result: Cascade of selling as trapped bulls exit + new shorts enter
Mirror image for failed bearish breakouts (trapped shorts cover + new longs enter).
Failure Detection Parameters: [/b>
1. Failure Confirmation Bars (default: 3): [/b>
How many bars after breakout to confirm failure?
Logic: Settings: [/b>
• 2 bars: Aggressive failure detection (more signals, more false failures)
• 3 bars Balanced (default)
• 5-10 bars: Conservative (wait for clear reversal)
Why This Matters:
Too few bars: You call "failed breakout" when price is just consolidating before next leg.
Too many bars: You miss the reversal entry (price already back in range).
2. Failure Buffer (default: 0.1 ATR): [/b>
How far inside ORB must price return to confirm failure?
Formula: Why Buffer Matters: clear rejection [/b> (not just hovering at level).
Settings: [/b>
• 0.0 ATR: No buffer, immediate failure signal
• 0.1 ATR: Small buffer (default) - filters noise
• [b>0.2-0.3 ATR: Large buffer - only dramatic failures count
Example: Reversal Entry System: [/b>
When failure confirmed, system generates complete reversal trade:
For Failed Bull Breakout (Short Reversal): [/b>
Entry: [/b> Current close when failure confirmed
Stop Loss: [/b> Extreme high since breakout + 0.10 ATR padding
Target 1: [/b> ORB High - (ORB Range × 0.5)
Target 2: Target 3: [/b> ORB High - (ORB Range × 1.5)
Example:
• ORB High: 5850, ORB Low: 5842, Range: 8 points
• Breakout to 5853, fails, reverses to 5848 (entry)
• Stop: 5853 + 1 = 5854 (6 point risk)
• T1: 5850 - 4 = 5846 (-2 points, 1:3 R:R)
• T2: 5850 - 8 = 5842 (-6 points, 1:1 R:R)
• T3: 5850 - 12 = 5838 (-10 points, 1.67:1 R:R)
[b>Why These Targets? [/b>
• T1 (0.5x ORB below high): Trapped bulls start panic
• T2 (1.0x ORB = ORB Mid): Major retracement, momentum fully reversed
• T3 (1.5x ORB): Reversal extended, now targeting opposite side
Historical Performance: [/b>
Failed breakout reversals in ORB Fusion's tracking system show:
• Win Rate: 65-75% (significantly higher than initial breakouts)
• Average Winner: 1.2x ORB range
• Average Loser: 0.5x ORB range (protected by stop at extreme)
• Expectancy: Strongly positive even with <70% win rate
Why Failed Breakouts Outperform: [/b>
1. Information Advantage: You now know what price did (failed to extend). Initial breakout trades are speculative; reversal trades are reactive to confirmed failure.
2. Trapped Participant Pressure: Every trapped bull becomes a seller. This creates sustained pressure.
3. Stop Loss Clarity: Extreme high is obvious stop (just beyond recent high). Breakout trades have ambiguous stops (ORB mid? Recent low? Too wide or too tight).
4. Mean Reversion Edge: Failed breakouts return to value (ORB mid). Initial breakouts try to escape value (harder to sustain).
Critical Insight: [/b>
"The best trade is often the one that trapped everyone else."
Failed breakouts create asymmetric opportunity because you're trading against [/b> trapped participants rather than with [/b> them. When you see a failed breakout signal, you're seeing real-time evidence that the market rejected directional conviction—that's exploitable.
📐 FIBONACCI EXTENSION SYSTEM
Six Extension Levels: [/b>
Extensions project how far price will travel after ORB breakout. Based on Fibonacci ratios + empirical market behavior.
1. 1.272x (27.2% Extension): [/b>
Formula: [/b> ORB High/Low + (ORB Range × 0.272)
Psychology: [/b> Initial probe beyond ORB. Early momentum + trapped shorts (on bull side) covering.
Probability of Reach: [/b> ~75-80% after confirmed breakout
Trading: [/b>
• First resistance/support after breakout
• Partial profit target (take 30-50% off)
• Watch for rejection here (could signal failure in progress)
Why 1.272? [/b> Related to harmonic patterns (1.272 is √1.618). Empirically, markets often stall at 25-30% extension before deciding whether to continue or fail.
2. 1.5x (50% Extension):
Formula: [/b> ORB High/Low + (ORB Range × 0.5)
Psychology: [/b> Breakout gaining conviction. Requires sustained buying/selling (not just momentum spike).
Probability of Reach: [/b> ~60-65% after confirmed breakout
Trading: [/b>
• Major partial profit (take 50-70% off)
• Move stops to breakeven
• Trail remaining position
Why 1.5x? [/b> Classic halfway point to 2.0x. Markets often consolidate here before final push. If day type is "Normal," this is likely the high/low for the day.
3. 1.618x (Golden Ratio Extension): [/b>
Formula: [/b> ORB High/Low + (ORB Range × 0.618)
Psychology: [/b> Strong directional day. Institutional conviction + retail FOMO.
Probability of Reach: [/b> ~45-50% after confirmed breakout
Trading: [/b>
• Final partial profit (close 80-90%)
• Trail remainder with wide stop (allow breathing room)
Why 1.618? [/b> Fibonacci golden ratio. Appears consistently in market geometry. When price reaches 1.618x extension, move is "mature" and reversal risk increases.
4. 2.0x (100% Extension): [/b>
Formula: ORB High/Low + (ORB Range × 1.0)
Psychology: [/b> Trend day confirmed. Opening range completely duplicated.
Probability of Reach: [/b> ~30-35% after confirmed breakout
Trading: Why 2.0x? [/b> Psychological level—range doubled. Also corresponds to typical daily ATR in many instruments (opening range ~ 0.5 ATR, daily range ~ 1.0 ATR).
5. 2.618x (Super Extension):
Formula: [/b> ORB High/Low + (ORB Range × 1.618)
Psychology: [/b> Parabolic move. News-driven or squeeze.
Probability of Reach: [/b> ~10-15% after confirmed breakout
[b>Trading: Why 2.618? [/b> Fibonacci ratio (1.618²). Rare to reach—when it does, move is extreme. Often precedes multi-day consolidation or reversal.
6. 3.0x (Extreme Extension): [/b>
Formula: [/b> ORB High/Low + (ORB Range × 2.0)
Psychology: [/b> Market melt-up/crash. Only in extreme events.
[b>Probability of Reach: [/b> <5% after confirmed breakout
Trading: [/b>
• Close immediately if reached
• These are outlier events (black swans, flash crashes, squeeze-outs)
• Holding for more is greed—take windfall profit
Why 3.0x? [/b> Triple opening range. So rare it's statistical noise. When it happens, it's headline news.
Visual Example:
ES futures, ORB 5842-5850 (8 point range), Bullish breakout:
• ORB High : 5850.00 (entry zone)
• 1.272x : 5850 + 2.18 = 5852.18 (first resistance)
• 1.5x : 5850 + 4.00 = 5854.00 (major target)
• 1.618x : 5850 + 4.94 = 5854.94 (strong target)
• 2.0x : 5850 + 8.00 = 5858.00 (trend day)
• 2.618x : 5850 + 12.94 = 5862.94 (extreme)
• 3.0x : 5850 + 16.00 = 5866.00 (parabolic)
Profit-Taking Strategy:
Optimal scaling out at extensions:
• Breakout entry at 5850.50
• 30% off at 1.272x (5852.18) → +1.68 points
• 40% off at 1.5x (5854.00) → +3.50 points
• 20% off at 1.618x (5854.94) → +4.44 points
• 10% off at 2.0x (5858.00) → +7.50 points
[b>Average Exit: Conclusion: [/b> Scaling out at extensions produces 40% higher expectancy than holding for home runs.
📊 GAP ANALYSIS & FILL PSYCHOLOGY
[b>Gap Definition: [/b>
Price discontinuity between previous close and current open:
• Gap Up : Open > Previous Close + noise threshold (0.1 ATR)
• Gap Down : Open < Previous Close - noise threshold
Why Gaps Matter: [/b>
Gaps represent unfilled orders [/b>. When market gaps up, all limit buy orders between yesterday's close and today's open are never filled. Those buyers are "left behind." Psychology: they wait for price to return ("fill the gap") so they can enter. This creates magnetic pull [/b> toward gap level.
Gap Fill Statistics (Empirical): [/b>
• Gaps <0.5% [/b>: 85-90% fill within same day
• Gaps 0.5-1.0% [/b>: 70-75% fill within same day, 90%+ within week
• Gaps >1.0% [/b>: 50-60% fill within same day (major news often prevents fill)
Gap Fill Strategy: [/b>
Setup 1: Gap-and-Go
Gap opens, extends away from gap (doesn't fill).
• ORB confirms direction away from gap
• Trade WITH ORB breakout direction
• Expectation: Gap won't fill today (momentum too strong)
Setup 2: Gap-Fill Fade
Gap opens, but fails to extend. Price drifts back toward gap.
• ORB breakout TOWARD gap (not away)
• Trade toward gap fill level
• Target: Previous close (gap fill complete)
Setup 3: Gap-Fill Rejection
Gap fills (touches previous close) then rejects.
• ORB breakout AWAY from gap after fill
• Trade away from gap direction
• Thesis: Gap filled (orders executed), now resume original direction
[b>Example: Scenario A (Gap-and-Go):
• ORB breaks upward to $454 (away from gap)
• Trade: LONG breakout, expect continued rally
• Gap becomes support ($452)
Scenario B (Gap-Fill):
• ORB breaks downward through $452.50 (toward gap)
• Trade: SHORT toward gap fill at $450.00
• Target: $450.00 (gap filled), close position
Scenario C (Gap-Fill Rejection):
• Price drifts to $450.00 (gap filled) early in session
• ORB establishes $450-$451 after gap fill
• ORB breaks upward to $451.50
• Trade: LONG breakout (gap is filled, now resume rally)
ORB Fusion Integration: [/b>
Dashboard shows:
• Gap type (Up/Down/None)
• Gap size (percentage)
• Gap fill status (Filled ✓ / Open)
This informs setup confidence:
• ORB breakout AWAY from unfilled gap: +10% confidence (gap becomes support/resistance)
• ORB breakout TOWARD unfilled gap: -10% confidence (gap fill may override ORB)
[b>📈 VWAP & INSTITUTIONAL BIAS [/b>
[b>Volume-Weighted Average Price (VWAP): [/b>
Average price weighted by volume at each price level. Represents true "average" cost for the day.
[b>Calculation: Institutional Benchmark [/b>: Institutions (mutual funds, pension funds) use VWAP as performance benchmark. If they buy above VWAP, they underperformed; below VWAP, they outperformed.
2. [b>Algorithmic Target [/b>: Many algos are programmed to buy below VWAP and sell above VWAP to achieve "fair" execution.
3. [b>Support/Resistance [/b>: VWAP acts as dynamic support (price above) or resistance (price below).
[b>VWAP Bands (Standard Deviations): [/b>
• [b>1σ Band [/b>: VWAP ± 1 standard deviation
- Contains ~68% of volume
- Normal trading range
- Bounces common
• [b>2σ Band [/b>: VWAP ± 2 standard deviations
- Contains ~95% of volume
- Extreme extension
- Mean reversion likely
ORB + VWAP Confluence: [/b>
Highest-probability setups occur when ORB and VWAP align:
Bullish Confluence: [/b>
• ORB breakout upward (bullish signal)
• Price above VWAP (institutional buying)
• Confidence boost: +15%
Bearish Confluence: [/b>
• ORB breakout downward (bearish signal)
• Price below VWAP (institutional selling)
• Confidence boost: +15%
[b>Divergence Warning:
• ORB breakout upward BUT price below VWAP
• Conflict: Breakout says "buy," VWAP says "sell"
• Confidence penalty: -10%
• Interpretation: Retail buying but institutions not participating (lower quality breakout)
📊 MOMENTUM CONTEXT SYSTEM
[b>Innovation: Candle Coloring by Position
Rather than fixed support/resistance lines, ORB Fusion colors candles based on their [b>relationship to ORB :
[b>Three Zones: [/b>
1. Inside ORB (Blue Boxes): [/b>
[b>Calculation:
• Darker blue: Near extremes of ORB (potential breakout imminent)
• Lighter blue: Near ORB mid (consolidation)
[b>Trading: [/b> Coiled spring—await breakout.
[b>2. Above ORB (Green Boxes):
[b>Calculation: 3. Below ORB (Red Boxes):
Mirror of above ORB logic.
[b>Special Contexts: [/b>
[b>Breakout Bar (Darkest Green/Red): [/b>
The specific bar where breakout occurs gets maximum color intensity regardless of distance. This highlights the pivotal moment.
[b>Failed Breakout Bar (Orange/Warning): [/b>
When failed breakout is confirmed, that bar gets orange/warning color. Visual alert: "reversal opportunity here."
[b>Near Extension (Cyan/Magenta Tint): [/b>
When price is within 0.5 ATR of an extension level, candle gets tinted cyan (bull) or magenta (bear). Indicates "target approaching—prepare to take profit."
[b>Why Visual Context? [/b>
Traditional indicators show lines. ORB Fusion shows [b>context-aware momentum [/b>. Glance at chart:
• Lots of blue? Consolidation day (fade extremes).
• Progressive green? Trend day (follow).
• Green then orange? Failed breakout (reversal setup).
This visual language communicates market state instantly—no interpretation needed.
🎯 TRADE SETUP GENERATION & GRADING [/b>
[b>Algorithmic Setup Detection: [/b>
ORB Fusion continuously evaluates market state and generates current best trade setup with:
• Action (LONG / SHORT / FADE HIGH / FADE LOW / WAIT)
• Entry price
• Stop loss
• Three targets
• Risk:Reward ratio
• Confidence score (0-100)
• Grade (A+ to D)
[b>Setup Types: [/b>
[b>1. ORB LONG (Bullish Breakout): [/b>
[b>Trigger: [/b>
• Bullish ORB breakout confirmed
• Not failed
[b>Parameters:
• Entry: Current close
• Stop: ORB mid (protects against failure)
• T1: ORB High + 0.5x range (1.5x extension)
• T2: ORB High + 1.0x range (2.0x extension)
• T3: ORB High + 1.618x range (2.618x extension)
[b>Confidence Scoring:
[b>Trigger: [/b>
• Bearish breakout occurred
• Failed (returned inside ORB)
[b>Parameters: [/b>
• Entry: Close when failure confirmed
• Stop: Extreme low since breakout + 0.10 ATR
• T1: ORB Low + 0.5x range
• T2: ORB Low + 1.0x range (ORB mid)
• T3: ORB Low + 1.5x range
[b>Confidence Scoring:
[b>Trigger:
• Inside ORB
• Close > ORB mid (near high)
[b>Parameters: [/b>
• Entry: ORB High (limit order)
• Stop: ORB High + 0.2x range
• T1: ORB Mid
• T2: ORB Low
[b>Confidence Scoring: [/b>
Base: 40 points (lower base—range fading is lower probability than breakout/reversal)
[b>Use Case: [/b> Rotation days. Not recommended on normal/trend days.
[b>6. FADE LOW (Range Trade):
Mirror of FADE HIGH.
[b>7. WAIT:
[b>Trigger: [/b>
• ORB not complete yet OR
• No clear setup (price in no-man's-land)
[b>Action: [/b> Observe, don't trade.
[b>Confidence: [/b> 0 points
[b>Grading System:
```
Confidence → Grade
85-100 → A+
75-84 → A
65-74 → B+
55-64 → B
45-54 → C
0-44 → D
```
[b>Grade Interpretation: [/b>
• [b>A+ / A: High probability setup. Take these trades.
• [b>B+ / B [/b>: Decent setup. Trade if fits system rules.
• [b>C [/b>: Marginal setup. Only if very experienced.
• [b>D [/b>: Poor setup or no setup. Don't trade.
[b>Example Scenario: [/b>
ES futures:
• ORB: 5842-5850 (8 point range)
• Bullish breakout to 5851 confirmed
• Volume: 2.0x average (confirmed)
• VWAP: 5845 (price above VWAP ✓)
• Day type: Developing (too early, no bonus)
• Gap: None
[b>Setup: [/b>
• Action: LONG
• Entry: 5851
• Stop: 5846 (ORB mid, -5 point risk)
• T1: 5854 (+3 points, 1:0.6 R:R)
• T2: 5858 (+7 points, 1:1.4 R:R)
• T3: 5862.94 (+11.94 points, 1:2.4 R:R)
[b>Confidence: LONG with 55% confidence.
Interpretation: Solid setup, not perfect. Trade it if your system allows B-grade signals.
[b>📊 STATISTICS TRACKING & PERFORMANCE ANALYSIS [/b>
[b>Real-Time Performance Metrics: [/b>
ORB Fusion tracks comprehensive statistics over user-defined lookback (default 50 days):
[b>Breakout Performance: [/b>
• [b>Bull Breakouts: [/b> Total count, wins, losses, win rate
• [b>Bear Breakouts: [/b> Total count, wins, losses, win rate
[b>Win Definition: [/b> Breakout reaches ≥1.0x extension (doubles the opening range) before end of day.
[b>Example: [/b>
• ORB: 5842-5850 (8 points)
• Bull breakout at 5851
• Reaches 5858 (1.0x extension) by close
• Result: WIN
[b>Failed Breakout Performance: [/b>
• [b>Total Failed Breakouts [/b>: Count of breakouts that failed
• [b>Reversal Wins [/b>: Count where reversal trade reached target
• [b>Failed Reversal Win Rate [/b>: Wins / Total Failed
[b>Win Definition for Reversals: [/b>
• Failed bull → reversal short reaches ORB mid
• Failed bear → reversal long reaches ORB mid
[b>Extension Tracking: [/b>
• [b>Average Extension Reached [/b>: Mean of maximum extension achieved across all breakout days
• [b>Max Extension Overall [/b>: Largest extension ever achieved in lookback period
[b>Example: 🎨 THREE DISPLAY MODES
[b>Design Philosophy: [/b>
Not all traders need all features. Beginners want simplicity. Professionals want everything. ORB Fusion adapts.
[b>SIMPLE MODE: [/b>
[b>Shows: [/b>
• Primary ORB levels (High, Mid, Low)
• ORB box
• Breakout signals (triangles)
• Failed breakout signals (crosses)
• Basic dashboard (ORB status, breakout status, setup)
• VWAP
[b>Hides: [/b>
• Session ORBs (Asian, London, NY)
• IB levels and extensions
• ORB extensions beyond basic levels
• Gap analysis visuals
• Statistics dashboard
• Momentum candle coloring
• Narrative dashboard
[b>Use Case: [/b>
• Traders who want clean chart
• Focus on core ORB concept only
• Mobile trading (less screen space)
[b>STANDARD MODE:
[b>Shows Everything in Simple Plus: [/b>
• Session ORBs (Asian, London, NY)
• IB levels (high, low, mid)
• IB extensions
• ORB extensions (1.272x, 1.5x, 1.618x, 2.0x)
• Gap analysis and fill targets
• VWAP bands (1σ and 2σ)
• Momentum candle coloring
• Context section in dashboard
• Narrative dashboard
[b>Hides: [/b>
• Advanced extensions (2.618x, 3.0x)
• Detailed statistics dashboard
[b>Use Case: [/b>
• Most traders
• Balance between information and clarity
• Covers 90% of use cases
[b>ADVANCED MODE:
[b>Shows Everything:
• All session ORBs
• All IB levels and extensions
• All ORB extensions (including 2.618x and 3.0x)
• Full gap analysis
• VWAP with both 1σ and 2σ bands
• Momentum candle coloring
• Complete statistics dashboard
• Narrative dashboard
• All context metrics
[b>Use Case: [/b>
• Professional traders
• System developers
• Those who want maximum information density
[b>Switching Modes: [/b>
Single dropdown input: "Display Mode" → Simple / Standard / Advanced
Entire indicator adapts instantly. No need to toggle 20 individual settings.
📖 NARRATIVE DASHBOARD
[b>Innovation: Plain-English Market State [/b>
Most indicators show data. ORB Fusion explains what the data [b>means [/b>.
[b>Narrative Components: [/b>
[b>1. Phase: [/b>
• "📍 Building ORB..." (during ORB session)
• "📊 Trading Phase" (after ORB complete)
• "⏳ Pre-Market" (before ORB session)
[b>2. Status (Current Observation): [/b>
• "⚠️ Failed breakout - reversal likely"
• "🚀 Bullish momentum in play"
• "📉 Bearish momentum in play"
• "⚖️ Consolidating in range"
• "👀 Monitoring for setup"
[b>3. Next Level:
Tells you what to watch for:
• "🎯 1.5x @ 5854.00" (next extension target)
• "Watch ORB levels" (inside range, await breakout)
[b>4. Setup: [/b>
Current trade setup + grade:
• "LONG " (bullish breakout, A-grade)
• "🔥 SHORT REVERSAL " (failed bull breakout, A+-grade)
• "WAIT " (no setup)
[b>5. Reason: [/b>
Why this setup exists:
• "ORB Bullish Breakout"
• "Failed Bear Breakout - High Probability Reversal"
• "Range Fade - Near High"
[b>6. Tip (Market Insight):
Contextual advice:
• "🔥 TREND DAY - Trail stops" (day type is trending)
• "🔄 ROTATION - Fade extremes" (day type is rotating)
• "📊 Gap unfilled - magnet level" (gap creates target)
• "📈 Normal conditions" (no special context)
[b>Example Narrative:
```
📖 ORB Narrative
━━━━━━━━━━━━━━━━
Phase | 📊 Trading Phase
Status | 🚀 Bullish momentum in play
Next | 🎯 1.5x @ 5854.00
📈 Setup | LONG
Reason | ORB Bullish Breakout
💡 Tip | 🔥 TREND DAY - Trail stops
```
[b>Glance Interpretation: [/b>
"We're in trading phase. Bullish breakout happened (momentum in play). Next target is 1.5x extension at 5854. Current setup is LONG with A-grade. It's a trend day, so trail stops (don't take early profits)."
Complete market state communicated in 6 lines. No interpretation needed.
[b>Why This Matters:
Beginner traders struggle with "So what?" question. Indicators show lines and signals, but what does it mean [/b>? Narrative dashboard bridges this gap.
Professional traders benefit too—rapid context assessment during fast-moving markets. No time to analyze; glance at narrative, get action plan.
🔔 INTELLIGENT ALERT SYSTEM
[b>Four Alert Types: [/b>
[b>1. Breakout Alert: [/b>
[b>Trigger: [/b> ORB breakout confirmed (bull or bear)
[b>Message: [/b>
```
🚀 ORB BULLISH BREAKOUT
Price: 5851.00
Volume Confirmed
Grade: A
```
[b>Frequency: [/b> Once per bar (prevents spam)
[b>2. Failed Breakout Alert: [/b>
[b>Trigger: [/b> Breakout fails, reversal setup generated
[b>Message: [/b>
```
🔥 FAILED BULLISH BREAKOUT!
HIGH PROBABILITY SHORT REVERSAL
Entry: 5848.00
Stop: 5854.00
T1: 5846.00
T2: 5842.00
Historical Win Rate: 73%
```
[b>Why Comprehensive? [/b> Failed breakout alerts include complete trade plan. You can execute immediately from alert—no need to check chart.
[b>3. Extension Alert:
[b>Trigger: [/b> Price reaches extension level for first time
[b>Message: [/b>
```
🎯 Bull Extension 1.5x reached @ 5854.00
```
[b>Use: [/b> Profit-taking reminder. When extension hit, consider scaling out.
[b>4. IB Break Alert: [/b>
[b>Trigger: [/b> Price breaks above IB high or below IB low
[b>Message: [/b>
```
📊 IB HIGH BROKEN - Potential Trend Day
```
[b>Use: [/b> Day type classification. IB break suggests trend day developing—adjust strategy to trend-following mode.
[b>Alert Management: [/b>
Each alert type can be enabled/disabled independently. Prevents notification overload.
[b>Cooldown Logic: [/b>
Alerts won't fire if same alert type triggered within last bar. Prevents:
• "Breakout" alert every tick during choppy breakout
• Multiple "extension" alerts if price oscillates at level
Ensures: One clean alert per event.
⚙️ KEY PARAMETERS EXPLAINED
[b>Opening Range Settings: [/b>
• [b>ORB Timeframe [/b> (5/15/30/60 min): Duration of opening range window
- 30 min recommended for most traders
• [b>Use RTH Only [/b> (ON/OFF): Only trade during regular trading hours
- ON recommended (avoids thin overnight markets)
• [b>Use LTF Precision [/b> (ON/OFF): Sample 1-minute bars for accuracy
- ON recommended (critical for charts >1 minute)
• [b>Precision TF [/b> (1/5 min): Timeframe for LTF sampling
- 1 min recommended (most accurate)
[b>Session ORBs: [/b>
• [b>Show Asian/London/NY ORB [/b> (ON/OFF): Display multi-session ranges
- OFF in Simple mode
- ON in Standard/Advanced if trading 24hr markets
• [b>Session Windows [/b>: Time ranges for each session ORB
- Defaults align with major session opens
[b>Initial Balance: [/b>
• [b>Show IB [/b> (ON/OFF): Display Initial Balance levels
- ON recommended for day type classification
• [b>IB Session Window [/b> (0930-1030): First hour of trading
- Default is standard for US equities
• [b>Show IB Extensions [/b> (ON/OFF): Project IB extension targets
- ON recommended (identifies trend days)
• [b>IB Extensions 1-4 [/b> (0.5x, 1.0x, 1.5x, 2.0x): Extension multipliers
- Defaults are Market Profile standard
[b>ORB Extensions: [/b>
• [b>Show Extensions [/b> (ON/OFF): Project ORB extension targets
- ON recommended (defines profit targets)
• [b>Enable Individual Extensions [/b> (1.272x, 1.5x, 1.618x, 2.0x, 2.618x, 3.0x)
- Enable 1.272x, 1.5x, 1.618x, 2.0x minimum
- Disable 2.618x and 3.0x unless trading very volatile instruments
[b>Breakout Detection:
• [b>Confirmation Method [/b> (Close/Wick/Body):
- Close recommended (best balance)
- Wick for scalping
- Body for conservative
• [b>Require Volume Confirmation [/b> (ON/OFF):
- ON recommended (increases reliability)
• [b>Volume Multiplier [/b> (1.0-3.0):
- 1.5x recommended
- Lower for thin instruments
- Higher for heavy volume instruments
[b>Failed Breakout System: [/b>
• [b>Enable Failed Breakouts [/b> (ON/OFF):
- ON strongly recommended (highest edge)
• [b>Bars to Confirm Failure [/b> (2-10):
- 3 bars recommended
- 2 for aggressive (more signals, more false failures)
- 5+ for conservative (fewer signals, higher quality)
• [b>Failure Buffer [/b> (0.0-0.5 ATR):
- 0.1 ATR recommended
- Filters noise during consolidation near ORB level
• [b>Show Reversal Targets [/b> (ON/OFF):
- ON recommended (visualizes trade plan)
• [b>Reversal Target Mults [/b> (0.5x, 1.0x, 1.5x):
- Defaults are tested values
- Adjust based on average daily range
[b>Gap Analysis:
• [b>Show Gap Analysis [/b> (ON/OFF):
- ON if trading instruments that gap frequently
- OFF for 24hr markets (forex, crypto—no gaps)
• [b>Gap Fill Target [/b> (ON/OFF):
- ON to visualize previous close (gap fill level)
[b>VWAP:
• [b>Show VWAP [/b> (ON/OFF):
- ON recommended (key institutional level)
• [b>Show VWAP Bands [/b> (ON/OFF):
- ON in Standard/Advanced
- OFF in Simple
• [b>Band Multipliers (1.0σ, 2.0σ):
- Defaults are standard
- 1σ = normal range, 2σ = extreme
[b>Day Type: [/b>
• [b>Show Day Type Analysis [/b> (ON/OFF):
- ON recommended (critical for strategy adaptation)
• [b>Trend Day Threshold [/b> (1.0-2.5 IB mult):
- 1.5x recommended
- When price extends >1.5x IB, classifies as Trend Day
[b>Enhanced Visuals:
• [b>Show Momentum Candles [/b> (ON/OFF):
- ON for visual context
- OFF if chart gets too colorful
• [b>Show Gradient Zone Fills [/b> (ON/OFF):
- ON for professional look
- OFF for minimalist chart
• [b>Label Display Mode [/b> (All/Adaptive/Minimal):
- Adaptive recommended (shows nearby labels only)
- All for information density
- Minimal for clean chart
• [b>Label Proximity [/b> (1.0-5.0 ATR):
- 3.0 ATR recommended
- Labels beyond this distance are hidden (Adaptive mode)
[b>🎓 PROFESSIONAL USAGE PROTOCOL [/b>
[b>Phase 1: Learning the System (Week 1) [/b>
[b>Goal: [/b> Understand ORB concepts and dashboard interpretation
[b>Setup: [/b>
• Display Mode: STANDARD
• ORB Timeframe: 30 minutes
• Enable ALL features (IB, extensions, failed breakouts, VWAP, gap analysis)
• Enable statistics tracking
[b>Actions: [/b>
• Paper trade ONLY—no real money
• Observe ORB formation every day (9:30-10:00 AM ET for US markets)
• Note when ORB breakouts occur and if they extend
• Note when breakouts fail and reversals happen
• Watch day type classification evolve during session
• Track statistics—which setups are working?
[b>Key Learning: [/b>
• How often do breakouts reach 1.5x extension? (typically 50-60% of confirmed breakouts)
• How often do breakouts fail? (typically 30-40%)
• Which setup grade (A/B/C) actually performs best? (should see A-grade outperforming)
• What day type produces best results? (trend days favor breakouts, rotation days favor fades)
[b>Phase 2: Parameter Optimization (Week 2) [/b>
[b>Goal: [/b> Tune system to your instrument and timeframe
[b>ORB Timeframe Selection:
• Run 5 days with 15-minute ORB
• Run 5 days with 30-minute ORB
• Compare: Which captures better breakouts on your instrument?
• Typically: 30-minute optimal for most, 15-minute for very liquid (ES, SPY)
[b>Volume Confirmation Testing:
• Run 5 days WITH volume confirmation
• Run 5 days WITHOUT volume confirmation
• Compare: Does volume confirmation increase win rate?
• If win rate improves by >5%: Keep volume confirmation ON
• If no improvement: Turn OFF (avoid missing valid breakouts)
[b>Failed Breakout Bars:
[b>Goal: [/b> Develop personal trading rules based on system signals
[b>Setup Selection Rules: [/b>
Define which setups you'll trade:
• [b>Conservative: [/b> Only A+ and A grades
• [b>Balanced: [/b> A+, A, B+ grades
• [b>Aggressive: [/b> All grades B and above
Test each approach for 5-10 trades, compare results.
[b>Position Sizing by Grade: [/b>
Consider risk-weighting by setup quality:
• A+ grade: 100% position size
• A grade: 75% position size
• B+ grade: 50% position size
• B grade: 25% position size
Example: If max risk is $1000/trade:
• A+ setup: Risk $1000
• A setup: Risk $750
• B+ setup: Risk $500
This matches bet sizing to edge.
[b>Day Type Adaptation: [/b>
Create rules for different day types:
Trend Days:
• Take ALL breakout signals (A/B/C grades)
• Hold for 2.0x extension minimum
• Trail stops aggressively (1.0 ATR trail)
• DON'T fade—reversals unlikely
Rotation Days:
• ONLY take failed breakout reversals
• Ignore initial breakout signals (likely to fail)
• Take profits quickly (0.5x extension)
• Focus on fade setups (Fade High/Fade Low)
Normal Days:
• Take A/A+ breakout signals only
• Take ALL failed breakout reversals (high probability)
• Target 1.0-1.5x extensions
• Partial profit-taking at extensions
Time-of-Day Rules: [/b>
Breakouts at different times have different probabilities:
10:00-10:30 AM (Early Breakout):
• ORB just completed
• Fresh breakout
• Probability: Moderate (50-55% reach 1.0x)
• Strategy: Conservative position sizing
10:30-12:00 PM (Mid-Morning):
• Momentum established
• Volume still healthy
• Probability: High (60-65% reach 1.0x)
• Strategy: Standard position sizing
12:00-2:00 PM (Lunch Doldrums):
• Volume dries up
• Whipsaw risk increases
• Probability: Low (40-45% reach 1.0x)
• Strategy: Avoid new entries OR reduce size 50%
2:00-4:00 PM (Afternoon Session):
• Late-day positioning
• EOD squeezes possible
• Probability: Moderate-High (55-60%)
• Strategy: Watch for IB break—if trending all day, follow
[b>Phase 4: Live Micro-Sizing (Month 2) [/b>
[b>Goal: [/b> Validate paper trading results with minimal risk
[b>Setup: [/b>
• 10-20% of intended full position size
• Take ONLY A+ and A grade setups
• Follow stop loss and targets religiously
[b>Execution: [/b>
• Execute from alerts OR from dashboard setup box
• Entry: Close of signal bar OR next bar market order
• Stop: Use exact stop from setup (don't widen)
• Targets: Scale out at T1/T2/T3 as indicated
[b>Tracking: [/b>
• Log every trade: Entry, Exit, Grade, Outcome, Day Type
• Calculate: Win rate, Average R-multiple, Max consecutive losses
• Compare to paper trading results (should be within 15%)
[b>Red Flags: [/b>
• Win rate <45%: System not suitable for this instrument/timeframe
• Major divergence from paper trading: Execution issues (slippage, late entries, emotional exits)
• Max consecutive losses >8: Hitting rough patch OR market regime changed
[b>Phase 5: Scaling Up (Months 3-6)
[b>Goal: [/b> Gradually increase to full position size
[b>Progression: [/b>
• Month 3: 25-40% size (if micro-sizing profitable)
• Month 4: 40-60% size
• Month 5: 60-80% size
• Month 6: 80-100% size
[b>Milestones Required to Scale Up: [/b>
• Minimum 30 trades at current size
• Win rate ≥48%
• Profit factor ≥1.2
• Max drawdown <20%
• Emotional control (no revenge trading, no FOMO)
[b>Advanced Techniques:
[b>Multi-Timeframe ORB: Assumes first 30-60 minutes establish value. Violation: Market opens after major news, price discovery continues for hours (opening range meaningless).
2. [b>Volume Indicates Conviction: ES, NQ, RTY, SPY, QQQ—high liquidity, clean ORB formation, reliable extensions
• [b>Large-Cap Stocks: AAPL, MSFT, TSLA, NVDA (>$5B market cap, >5M daily volume)
• [b>Liquid Futures: CL (crude oil), GC (gold), 6E (EUR/USD), ZB (bonds)—24hr markets benefit from session ORBs
• [b>Major Forex Pairs: [/b> EUR/USD, GBP/USD, USD/JPY—London/NY session ORBs work well
[b>Performs Poorly On: [/b>
• [b>Illiquid Stocks: <$1M daily volume, wide spreads, gappy price action
• [b>Penny Stocks: [/b> Manipulated, pump-and-dump, no real price discovery
• [b>Low-Volume ETFs: Exotic sector ETFs, leveraged products with thin volume
• [b>Crypto on Sketchy Exchanges: Wash trading, spoofing invalidates volume analysis
• [b>Earnings Days: [/b> ORB completes before earnings release, then completely resets (useless)
• Binary Event Days: FDA approvals, court rulings—discontinuous price action
[b>Known Weaknesses: [/b>
• [b>Slow Starts: ORB doesn't complete until 10:00 AM (30-min ORB). Early morning traders have no signals for 30 minutes. Consider using 15-minute ORB if this is problematic.
• [b>Failure Detection Lag: [/b> Failed breakout requires 3+ bars to confirm. By the time system signals reversal, price may have already moved significantly back inside range. Manual traders watching in real-time can enter earlier.
• [b>Extension Overshoot: [/b> System projects extensions mathematically (1.5x, 2.0x, etc.). Actual moves may stop short (1.3x) or overshoot (2.2x). Extensions are targets, not magnets.
• [b>Day Type Misclassification: [/b> Early in session, day type is "Developing." By the time it's classified definitively (often 11:00 AM+), half the day is over. Strategy adjustments happen late.
• [b>Gap Assumptions: [/b> System assumes gaps want to fill. Strong trend days never fill gaps (gap becomes support/resistance forever). Blindly trading toward gaps can backfire on trend days.
• [b>Volume Data Quality: Forex doesn't have centralized volume (uses tick volume as proxy—less reliable). Crypto volume is often fake (wash trading). Volume confirmation less effective on these instruments.
• [b>Multi-Session Complexity: [/b> When using Asian/London/NY ORBs simultaneously, chart becomes cluttered. Requires discipline to focus on relevant session for current time.
[b>Risk Factors: [/b>
• [b>Opening Gaps: Large gaps (>2%) can create distorted ORBs. Opening range might be unusually wide or narrow, making extensions unreliable.
• [b>Low Volatility Environments:[/b> When VIX <12, opening ranges can be tiny (0.2-0.3%). Extensions are equally tiny. Profit targets don't justify commission/slippage.
• [b>High Volatility Environments:[/b> When VIX >30, opening ranges are huge (2-3%+). Extensions project unrealistic targets. Failed breakouts happen faster (volatility whipsaw).
• [b>Algorithm Dominance:[/b> In heavily algorithmic markets (ES during overnight session), ORB levels can be manipulated—algos pin price to ORB high/low intentionally. Breakouts become stop-runs rather than genuine directional moves.
[b>⚠️ RISK DISCLOSURE[/b>
Trading futures, stocks, options, forex, and cryptocurrencies involves substantial risk of loss and is not suitable for all investors. Opening Range Breakout strategies, while based on sound market structure principles, do not guarantee profits and can result in significant losses.
The ORB Fusion indicator implements professional trading concepts including Opening Range theory, Market Profile Initial Balance analysis, Fibonacci extensions, and failed breakout reversal logic. These methodologies have theoretical foundations but past performance—whether backtested or live—is not indicative of future results.
Opening Range theory assumes the first 30-60 minutes of trading establish a meaningful value area and that breakouts from this range signal directional conviction. This assumption may not hold during:
• Major news events (FOMC, NFP, earnings surprises)
• Market structure changes (circuit breakers, trading halts)
• Low liquidity periods (holidays, early closures)
• Algorithmic manipulation or spoofing
Failed breakout detection relies on patterns of trapped participant behavior. While historically these patterns have shown statistical edges, market conditions change. Institutional algorithms, changing market structure, or regime shifts can reduce or eliminate edges that existed historically.
Initial Balance classification (trend day vs rotation day vs normal day) is a heuristic framework, not a deterministic prediction. Day type can change mid-session. Early classification may prove incorrect as the day develops.
Extension projections (1.272x, 1.5x, 1.618x, 2.0x, etc.) are probabilistic targets derived from Fibonacci ratios and empirical market behavior. They are not "support and resistance levels" that price must reach or respect. Markets can stop short of extensions, overshoot them, or ignore them entirely.
Volume confirmation assumes high volume indicates institutional participation and conviction. In algorithmic markets, volume can be artificially high (HFT activity) or artificially low (dark pools, internalization). Volume is a proxy, not a guarantee of conviction.
LTF precision sampling improves ORB accuracy by using 1-minute bars but introduces additional data dependencies. If 1-minute data is unavailable, inaccurate, or delayed, ORB calculations will be incorrect.
The grading system (A+/A/B+/B/C/D) and confidence scores aggregate multiple factors (volume, VWAP, day type, IB expansion, gap context) into a single assessment. This is a mechanical calculation, not artificial intelligence. The system cannot adapt to unprecedented market conditions or events outside its programmed logic.
Real trading involves slippage, commissions, latency, partial fills, and rejected orders not present in indicator calculations. ORB Fusion generates signals at bar close; actual fills occur with delay. Opening range forms during highest volatility (first 30 minutes)—spreads widen, slippage increases. Execution quality significantly impacts realized results.
Statistics tracking (win rates, extension levels reached, day type distribution) is based on historical bars in your lookback window. If lookback is small (<50 bars) or market regime changed, statistics may not represent future probabilities.
Users must independently validate system performance on their specific instruments, timeframes, and broker execution environment. Paper trade extensively (100+ trades minimum) before risking capital. Start with micro position sizing (5-10% of intended size) for 50+ trades to validate execution quality matches expectations.
Never risk more than you can afford to lose completely. Use proper position sizing (0.5-2% risk per trade maximum). Implement stop losses on every single trade without exception. Understand that most retail traders lose money—sophisticated indicators do not change this fundamental reality. They systematize analysis but cannot eliminate risk.
The developer makes no warranties regarding profitability, suitability, accuracy, reliability, or fitness for any purpose. Users assume full responsibility for all trading decisions, parameter selections, risk management, and outcomes.
By using this indicator, you acknowledge that you have read, understood, and accepted these risk disclosures and limitations, and you accept full responsibility for all trading activity and potential losses.
[b>═══════════════════════════════════════════════════════════════════════════════[/b>
[b>CLOSING STATEMENT[/b>
[b>═══════════════════════════════════════════════════════════════════════════════[/b>
Opening Range Breakout is not a trick. It's a framework. The first 30-60 minutes reveal where participants believe value lies. Breakouts signal directional conviction. Failures signal trapped participants. Extensions define profit targets. Day types dictate strategy. Failed breakouts create the highest-probability reversals.
ORB Fusion doesn't predict the future—it identifies [b>structure[/b>, detects [b>breakouts[/b>, recognizes [b>failures[/b>, and generates [b>probabilistic trade plans[/b> with defined risk and reward.
The edge is not in the opening range itself. The edge is in recognizing when the market respects structure (follow breakouts) versus when it violates structure (fade breakouts). The edge is in detecting failures faster than discretionary traders. The edge is in systematic classification that prevents catastrophic errors—like fading a trend day or holding through rotation.
Most indicators draw lines. ORB Fusion implements a complete institutional trading methodology: Opening Range theory, Market Profile classification, failed breakout intelligence, Fibonacci projections, volume confirmation, gap psychology, and real-time performance tracking.
Whether you're a beginner learning market structure or a professional seeking systematic ORB implementation, this system provides the framework.
"The market's first word is its opening range. Everything after is commentary." — ORB Fusion
Beta Coefficient & RSI Table (Midcaps vs Majors)Beta Coefficient & RSI Table (Midcaps vs Majors)
This script builds a comprehensive beta comparison framework between midcap assets and majors for benchmarks, enhanced with a simple RSI midline strategy for clean entry and exit signaling.
In addition to beta-based relative analysis, the script:
Computes raw RSI values on midcap assets for standalone trend qualification
Evaluates every midcap/major ratio combination using the same RSI-based regime logic
Produces binary (0 / 1) signals suitable for systematic filtering and automation
Designed with automation in mind, this script is perfect for daily alerts that can send webhooks externally, and is fully compatible to reliably daily close updates for:
Ratio beta comparisons (midcaps vs majors)
Binary RSI crossover signals on each ratio
Base midcap trend state (RSI > 45 indicating an active uptrend) - 45 made for a slightly faster entry signal if used as a preliminary filter
This makes the table ideal for automated system building, signal aggregates, and hands-off portfolio logic.
Full credits to @MarktQuant and @NianiaFrania🐸 for the original script source.
Neeson Mayer MultipleIntegrating the Mayer Multiple Indicator: A Practical Guide for Market Analysis
Introduction
The Mayer Multiple indicator is a specialized tool designed to assess asset valuations relative to their long-term historical trends. By comparing current price action against a long-term simple moving average, this indicator provides a quantitative framework for identifying potential overbought and oversold conditions. This article explains the rationale behind its design, operational mechanics, practical applications, and unique value proposition.
Purpose and Functionality
The primary function of the Mayer Multiple indicator is to measure how far current prices deviate from a long-term moving average, expressed as a ratio. This measurement helps traders and investors identify:
Extreme valuation levels that may signal potential reversal points
Long-term trend strength and sustainability
Market psychology shifts between fear and greed cycles
Originally popularized in Bitcoin analysis, the indicator's principles apply to any volatile asset class where mean reversion tendencies exist alongside strong trend characteristics.
Operational Principles
The indicator operates through several interconnected components:
Core Calculation Mechanism
At its heart, the indicator calculates the Mayer Multiple by dividing the current closing price by a configurable simple moving average (default: 200 periods). This ratio represents how many times the current price exceeds its long-term average, providing an immediate visual reference for valuation extremes.
Multi-Level Threshold System
Four configurable thresholds create distinct market condition zones:
Optimal Buy Zone (default: 0.7) - Historically extreme undervaluation
Undervalued Zone (default: 1.0) - Moderate undervaluation
Overvalued Zone (default: 2.4) - Moderate overvaluation
Optimal Sell Zone (default: 3.5) - Historically extreme overvaluation
These thresholds create a graduated scale of market conditions rather than binary signals.
Visual Signal Hierarchy
A sophisticated color-coding system prioritizes different signal types based on their significance:
White/Gray: Neutral territory (between undervalued and overvalued thresholds)
Aqua: Entering undervalued territory (potential accumulation zone)
White: Reaching optimal buying conditions (historically rare opportunities)
Yellow: Entering overvalued territory (potential distribution zone)
Orange: Reaching optimal selling conditions (historically rare extremes)
Green: Emerging from optimal buying conditions (momentum shift confirmation)
Red: Retreating from optimal selling conditions (momentum reversal confirmation)
This hierarchy helps users distinguish between entry signals, exit signals, and confirmation signals.
Integration Rationale
The integration of these components follows a logical progression:
Mathematical Foundation
The moving average provides a stable reference point that filters out short-term noise while maintaining sensitivity to long-term trend changes. The ratio format normalizes values across different price levels and timeframes, enabling cross-asset comparisons.
Behavioral Finance Alignment
The threshold system corresponds to documented market psychology patterns. The extreme thresholds (optimal buy/sell) represent points where fear or greed typically reach maximum intensity, while the moderate thresholds represent early warning levels.
Progressive Signal Detection
The indicator tracks both threshold breaches and retreats from extreme zones. This dual-tracking approach captures not only when conditions become extreme but also when they begin to normalize—often the most actionable moments for position adjustments.
Component Synergy
The indicator's components work together through a continuous feedback loop:
Calculation Engine: Continuously computes the core ratio, serving as the foundation for all subsequent analysis.
Threshold Comparator: Compares the current ratio against user-defined thresholds, categorizing market conditions in real-time.
Signal Generator: Identifies specific events (threshold crossings, zone entries/exits) and assigns appropriate visual representations.
Visual Renderer: Displays the information through colored histograms, reference lines, and data tables, creating an intuitive interface.
Alert System: Monitors for predefined conditions and notifies users of significant developments without requiring constant screen monitoring.
This integrated approach transforms raw price data into structured, actionable information while maintaining mathematical rigor and visual clarity.
Practical Application Guidelines
Parameter Customization
Users should adjust parameters based on:
Asset volatility (higher volatility assets may require wider thresholds)
Timeframe (longer timeframes may benefit from longer moving averages)
Personal risk tolerance (conservative traders may use tighter thresholds)
Signal Interpretation Framework
Zone-Based Analysis: Focus on which zone the indicator occupies rather than chasing individual data points
Confirmation Seeking: Use extreme zone signals (white/orange) as alerts for further analysis rather than automatic trade triggers
Momentum Assessment: Observe how quickly the indicator moves between zones as a measure of trend strength
Complementary Tools
The Mayer Multiple works best when combined with:
Volume analysis to confirm participation during extreme readings
Momentum indicators to identify potential divergence
Support/resistance levels for precise entry/exit timing
Fundamental analysis for context validation
Distinctive Attributes
Original Implementation Features
Progressive Color System: Unlike binary indicators, this implementation provides graduated signals through a carefully prioritized color hierarchy.
Dual-Signal Detection: The indicator captures both threshold breaches and retreats, offering insights into momentum shifts rather than just static levels.
Contextual Display: The integrated data table provides immediate access to key metrics without cluttering the chart space.
Customizable Framework: All thresholds and calculation periods are adjustable, allowing adaptation to different market regimes and trading styles.
Practical Innovation
The indicator's design emphasizes usability through:
Immediate visual comprehension via color coding
Clear separation between alert conditions and confirmation signals
Balanced information density (sufficient data without overload)
Flexible integration with existing trading workflows
Responsible Usage Considerations
Empirical Perspective
Historical analysis suggests that assets frequently revert toward their long-term moving averages, but the timing and extent of such reversions vary significantly. The indicator identifies statistical extremes rather than predicting immediate price movements.
Risk Management Integration
Users should:
Treat extreme readings as risk management triggers rather than directional forecasts
Consider position sizing based on distance from the moving average
Implement stop-loss strategies regardless of indicator readings
Avoid allocating excessive weight to any single indicator
Performance Realism
The indicator does not guarantee profitable outcomes. Its value lies in providing structured information about valuation extremes, which must be interpreted within broader market context and individual risk parameters.
Conclusion
The Mayer Multiple indicator represents a thoughtfully integrated approach to long-term valuation analysis. By combining mathematical rigor with behavioral insights and practical visualization, it provides traders with a structured framework for assessing market extremes. Its modular design allows customization while maintaining core analytical integrity, and its emphasis on graduated signals helps avoid the oversimplification common in technical indicators. When used as part of a comprehensive trading methodology with appropriate risk management, it can contribute valuable perspective to the decision-making process.
Dimensional Resonance ProtocolDimensional Resonance Protocol
🌀 CORE INNOVATION: PHASE SPACE RECONSTRUCTION & EMERGENCE DETECTION
The Dimensional Resonance Protocol represents a paradigm shift from traditional technical analysis to complexity science. Rather than measuring price levels or indicator crossovers, DRP reconstructs the hidden attractor governing market dynamics using Takens' embedding theorem, then detects emergence —the rare moments when multiple dimensions of market behavior spontaneously synchronize into coherent, predictable states.
The Complexity Hypothesis:
Markets are not simple oscillators or random walks—they are complex adaptive systems existing in high-dimensional phase space. Traditional indicators see only shadows (one-dimensional projections) of this higher-dimensional reality. DRP reconstructs the full phase space using time-delay embedding, revealing the true structure of market dynamics.
Takens' Embedding Theorem (1981):
A profound mathematical result from dynamical systems theory: Given a time series from a complex system, we can reconstruct its full phase space by creating delayed copies of the observation.
Mathematical Foundation:
From single observable x(t), create embedding vectors:
X(t) =
Where:
• d = Embedding dimension (default 5)
• τ = Time delay (default 3 bars)
• x(t) = Price or return at time t
Key Insight: If d ≥ 2D+1 (where D is the true attractor dimension), this embedding is topologically equivalent to the actual system dynamics. We've reconstructed the hidden attractor from a single price series.
Why This Matters:
Markets appear random in one dimension (price chart). But in reconstructed phase space, structure emerges—attractors, limit cycles, strange attractors. When we identify these structures, we can detect:
• Stable regions : Predictable behavior (trade opportunities)
• Chaotic regions : Unpredictable behavior (avoid trading)
• Critical transitions : Phase changes between regimes
Phase Space Magnitude Calculation:
phase_magnitude = sqrt(Σ ² for i = 0 to d-1)
This measures the "energy" or "momentum" of the market trajectory through phase space. High magnitude = strong directional move. Low magnitude = consolidation.
📊 RECURRENCE QUANTIFICATION ANALYSIS (RQA)
Once phase space is reconstructed, we analyze its recurrence structure —when does the system return near previous states?
Recurrence Plot Foundation:
A recurrence occurs when two phase space points are closer than threshold ε:
R(i,j) = 1 if ||X(i) - X(j)|| < ε, else 0
This creates a binary matrix showing when the system revisits similar states.
Key RQA Metrics:
1. Recurrence Rate (RR):
RR = (Number of recurrent points) / (Total possible pairs)
• RR near 0: System never repeats (highly stochastic)
• RR = 0.1-0.3: Moderate recurrence (tradeable patterns)
• RR > 0.5: System stuck in attractor (ranging market)
• RR near 1: System frozen (no dynamics)
Interpretation: Moderate recurrence is optimal —patterns exist but market isn't stuck.
2. Determinism (DET):
Measures what fraction of recurrences form diagonal structures in the recurrence plot. Diagonals indicate deterministic evolution (trajectory follows predictable paths).
DET = (Recurrence points on diagonals) / (Total recurrence points)
• DET < 0.3: Random dynamics
• DET = 0.3-0.7: Moderate determinism (patterns with noise)
• DET > 0.7: Strong determinism (technical patterns reliable)
Trading Implication: Signals are prioritized when DET > 0.3 (deterministic state) and RR is moderate (not stuck).
Threshold Selection (ε):
Default ε = 0.10 × std_dev means two states are "recurrent" if within 10% of a standard deviation. This is tight enough to require genuine similarity but loose enough to find patterns.
🔬 PERMUTATION ENTROPY: COMPLEXITY MEASUREMENT
Permutation entropy measures the complexity of a time series by analyzing the distribution of ordinal patterns.
Algorithm (Bandt & Pompe, 2002):
1. Take overlapping windows of length n (default n=4)
2. For each window, record the rank order pattern
Example: → pattern (ranks from lowest to highest)
3. Count frequency of each possible pattern
4. Calculate Shannon entropy of pattern distribution
Mathematical Formula:
H_perm = -Σ p(π) · ln(p(π))
Where π ranges over all n! possible permutations, p(π) is the probability of pattern π.
Normalized to :
H_norm = H_perm / ln(n!)
Interpretation:
• H < 0.3 : Very ordered, crystalline structure (strong trending)
• H = 0.3-0.5 : Ordered regime (tradeable with patterns)
• H = 0.5-0.7 : Moderate complexity (mixed conditions)
• H = 0.7-0.85 : Complex dynamics (challenging to trade)
• H > 0.85 : Maximum entropy (nearly random, avoid)
Entropy Regime Classification:
DRP classifies markets into five entropy regimes:
• CRYSTALLINE (H < 0.3): Maximum order, persistent trends
• ORDERED (H < 0.5): Clear patterns, momentum strategies work
• MODERATE (H < 0.7): Mixed dynamics, adaptive required
• COMPLEX (H < 0.85): High entropy, mean reversion better
• CHAOTIC (H ≥ 0.85): Near-random, minimize trading
Why Permutation Entropy?
Unlike traditional entropy methods requiring binning continuous data (losing information), permutation entropy:
• Works directly on time series
• Robust to monotonic transformations
• Computationally efficient
• Captures temporal structure, not just distribution
• Immune to outliers (uses ranks, not values)
⚡ LYAPUNOV EXPONENT: CHAOS vs STABILITY
The Lyapunov exponent λ measures sensitivity to initial conditions —the hallmark of chaos.
Physical Meaning:
Two trajectories starting infinitely close will diverge at exponential rate e^(λt):
Distance(t) ≈ Distance(0) × e^(λt)
Interpretation:
• λ > 0 : Positive Lyapunov exponent = CHAOS
- Small errors grow exponentially
- Long-term prediction impossible
- System is sensitive, unpredictable
- AVOID TRADING
• λ ≈ 0 : Near-zero = CRITICAL STATE
- Edge of chaos
- Transition zone between order and disorder
- Moderate predictability
- PROCEED WITH CAUTION
• λ < 0 : Negative Lyapunov exponent = STABLE
- Small errors decay
- Trajectories converge
- System is predictable
- OPTIMAL FOR TRADING
Estimation Method:
DRP estimates λ by tracking how quickly nearby states diverge over a rolling window (default 20 bars):
For each bar i in window:
δ₀ = |x - x | (initial separation)
δ₁ = |x - x | (previous separation)
if δ₁ > 0:
ratio = δ₀ / δ₁
log_ratios += ln(ratio)
λ ≈ average(log_ratios)
Stability Classification:
• STABLE : λ < 0 (negative growth rate)
• CRITICAL : |λ| < 0.1 (near neutral)
• CHAOTIC : λ > 0.2 (strong positive growth)
Signal Filtering:
By default, NEXUS requires λ < 0 (stable regime) for signal confirmation. This filters out trades during chaotic periods when technical patterns break down.
📐 HIGUCHI FRACTAL DIMENSION
Fractal dimension measures self-similarity and complexity of the price trajectory.
Theoretical Background:
A curve's fractal dimension D ranges from 1 (smooth line) to 2 (space-filling curve):
• D ≈ 1.0 : Smooth, persistent trending
• D ≈ 1.5 : Random walk (Brownian motion)
• D ≈ 2.0 : Highly irregular, space-filling
Higuchi Method (1988):
For a time series of length N, construct k different curves by taking every k-th point:
L(k) = (1/k) × Σ|x - x | × (N-1)/(⌊(N-m)/k⌋ × k)
For different values of k (1 to k_max), calculate L(k). The fractal dimension is the slope of log(L(k)) vs log(1/k):
D = slope of log(L) vs log(1/k)
Market Interpretation:
• D < 1.35 : Strong trending, persistent (Hurst > 0.5)
- TRENDING regime
- Momentum strategies favored
- Breakouts likely to continue
• D = 1.35-1.45 : Moderate persistence
- PERSISTENT regime
- Trend-following with caution
- Patterns have meaning
• D = 1.45-1.55 : Random walk territory
- RANDOM regime
- Efficiency hypothesis holds
- Technical analysis least reliable
• D = 1.55-1.65 : Anti-persistent (mean-reverting)
- ANTI-PERSISTENT regime
- Oscillator strategies work
- Overbought/oversold meaningful
• D > 1.65 : Highly complex, choppy
- COMPLEX regime
- Avoid directional bets
- Wait for regime change
Signal Filtering:
Resonance signals (secondary signal type) require D < 1.5, indicating trending or persistent dynamics where momentum has meaning.
🔗 TRANSFER ENTROPY: CAUSAL INFORMATION FLOW
Transfer entropy measures directed causal influence between time series—not just correlation, but actual information transfer.
Schreiber's Definition (2000):
Transfer entropy from X to Y measures how much knowing X's past reduces uncertainty about Y's future:
TE(X→Y) = H(Y_future | Y_past) - H(Y_future | Y_past, X_past)
Where H is Shannon entropy.
Key Properties:
1. Directional : TE(X→Y) ≠ TE(Y→X) in general
2. Non-linear : Detects complex causal relationships
3. Model-free : No assumptions about functional form
4. Lag-independent : Captures delayed causal effects
Three Causal Flows Measured:
1. Volume → Price (TE_V→P):
Measures how much volume patterns predict price changes.
• TE > 0 : Volume provides predictive information about price
- Institutional participation driving moves
- Volume confirms direction
- High reliability
• TE ≈ 0 : No causal flow (weak volume/price relationship)
- Volume uninformative
- Caution on signals
• TE < 0 (rare): Suggests price leading volume
- Potentially manipulated or thin market
2. Volatility → Momentum (TE_σ→M):
Does volatility expansion predict momentum changes?
• Positive TE : Volatility precedes momentum shifts
- Breakout dynamics
- Regime transitions
3. Structure → Price (TE_S→P):
Do support/resistance patterns causally influence price?
• Positive TE : Structural levels have causal impact
- Technical levels matter
- Market respects structure
Net Causal Flow:
Net_Flow = TE_V→P + 0.5·TE_σ→M + TE_S→P
• Net > +0.1 : Bullish causal structure
• Net < -0.1 : Bearish causal structure
• |Net| < 0.1 : Neutral/unclear causation
Causal Gate:
For signal confirmation, NEXUS requires:
• Buy signals : TE_V→P > 0 AND Net_Flow > 0.05
• Sell signals : TE_V→P > 0 AND Net_Flow < -0.05
This ensures volume is actually driving price (causal support exists), not just correlated noise.
Implementation Note:
Computing true transfer entropy requires discretizing continuous data into bins (default 6 bins) and estimating joint probability distributions. NEXUS uses a hybrid approach combining TE theory with autocorrelation structure and lagged cross-correlation to approximate information transfer in computationally efficient manner.
🌊 HILBERT PHASE COHERENCE
Phase coherence measures synchronization across market dimensions using Hilbert transform analysis.
Hilbert Transform Theory:
For a signal x(t), the Hilbert transform H (t) creates an analytic signal:
z(t) = x(t) + i·H (t) = A(t)·e^(iφ(t))
Where:
• A(t) = Instantaneous amplitude
• φ(t) = Instantaneous phase
Instantaneous Phase:
φ(t) = arctan(H (t) / x(t))
The phase represents where the signal is in its natural cycle—analogous to position on a unit circle.
Four Dimensions Analyzed:
1. Momentum Phase : Phase of price rate-of-change
2. Volume Phase : Phase of volume intensity
3. Volatility Phase : Phase of ATR cycles
4. Structure Phase : Phase of position within range
Phase Locking Value (PLV):
For two signals with phases φ₁(t) and φ₂(t), PLV measures phase synchronization:
PLV = |⟨e^(i(φ₁(t) - φ₂(t)))⟩|
Where ⟨·⟩ is time average over window.
Interpretation:
• PLV = 0 : Completely random phase relationship (no synchronization)
• PLV = 0.5 : Moderate phase locking
• PLV = 1 : Perfect synchronization (phases locked)
Pairwise PLV Calculations:
• PLV_momentum-volume : Are momentum and volume cycles synchronized?
• PLV_momentum-structure : Are momentum cycles aligned with structure?
• PLV_volume-structure : Are volume and structural patterns in phase?
Overall Phase Coherence:
Coherence = (PLV_mom-vol + PLV_mom-struct + PLV_vol-struct) / 3
Signal Confirmation:
Emergence signals require coherence ≥ threshold (default 0.70):
• Below 0.70: Dimensions not synchronized, no coherent market state
• Above 0.70: Dimensions in phase, coherent behavior emerging
Coherence Direction:
The summed phase angles indicate whether synchronized dimensions point bullish or bearish:
Direction = sin(φ_momentum) + 0.5·sin(φ_volume) + 0.5·sin(φ_structure)
• Direction > 0 : Phases pointing upward (bullish synchronization)
• Direction < 0 : Phases pointing downward (bearish synchronization)
🌀 EMERGENCE SCORE: MULTI-DIMENSIONAL ALIGNMENT
The emergence score aggregates all complexity metrics into a single 0-1 value representing market coherence.
Eight Components with Weights:
1. Phase Coherence (20%):
Direct contribution: coherence × 0.20
Measures dimensional synchronization.
2. Entropy Regime (15%):
Contribution: (0.6 - H_perm) / 0.6 × 0.15 if H < 0.6, else 0
Rewards low entropy (ordered, predictable states).
3. Lyapunov Stability (12%):
• λ < 0 (stable): +0.12
• |λ| < 0.1 (critical): +0.08
• λ > 0.2 (chaotic): +0.0
Requires stable, predictable dynamics.
4. Fractal Dimension Trending (12%):
Contribution: (1.45 - D) / 0.45 × 0.12 if D < 1.45, else 0
Rewards trending fractal structure (D < 1.45).
5. Dimensional Resonance (12%):
Contribution: |dimensional_resonance| × 0.12
Measures alignment across momentum, volume, structure, volatility dimensions.
6. Causal Flow Strength (9%):
Contribution: |net_causal_flow| × 0.09
Rewards strong causal relationships.
7. Phase Space Embedding (10%):
Contribution: min(|phase_magnitude_norm|, 3.0) / 3.0 × 0.10 if |magnitude| > 1.0
Rewards strong trajectory in reconstructed phase space.
8. Recurrence Quality (10%):
Contribution: determinism × 0.10 if DET > 0.3 AND 0.1 < RR < 0.8
Rewards deterministic patterns with moderate recurrence.
Total Emergence Score:
E = Σ(components) ∈
Capped at 1.0 maximum.
Emergence Direction:
Separate calculation determining bullish vs bearish:
• Dimensional resonance sign
• Net causal flow sign
• Phase magnitude correlation with momentum
Signal Threshold:
Default emergence_threshold = 0.75 means 75% of maximum possible emergence score required to trigger signals.
Why Emergence Matters:
Traditional indicators measure single dimensions. Emergence detects self-organization —when multiple independent dimensions spontaneously align. This is the market equivalent of a phase transition in physics, where microscopic chaos gives way to macroscopic order.
These are the highest-probability trade opportunities because the entire system is resonating in the same direction.
🎯 SIGNAL GENERATION: EMERGENCE vs RESONANCE
DRP generates two tiers of signals with different requirements:
TIER 1: EMERGENCE SIGNALS (Primary)
Requirements:
1. Emergence score ≥ threshold (default 0.75)
2. Phase coherence ≥ threshold (default 0.70)
3. Emergence direction > 0.2 (bullish) or < -0.2 (bearish)
4. Causal gate passed (if enabled): TE_V→P > 0 and net_flow confirms direction
5. Stability zone (if enabled): λ < 0 or |λ| < 0.1
6. Price confirmation: Close > open (bulls) or close < open (bears)
7. Cooldown satisfied: bars_since_signal ≥ cooldown_period
EMERGENCE BUY:
• All above conditions met with bullish direction
• Market has achieved coherent bullish state
• Multiple dimensions synchronized upward
EMERGENCE SELL:
• All above conditions met with bearish direction
• Market has achieved coherent bearish state
• Multiple dimensions synchronized downward
Premium Emergence:
When signal_quality (emergence_score × phase_coherence) > 0.7:
• Displayed as ★ star symbol
• Highest conviction trades
• Maximum dimensional alignment
Standard Emergence:
When signal_quality 0.5-0.7:
• Displayed as ◆ diamond symbol
• Strong signals but not perfect alignment
TIER 2: RESONANCE SIGNALS (Secondary)
Requirements:
1. Dimensional resonance > +0.6 (bullish) or < -0.6 (bearish)
2. Fractal dimension < 1.5 (trending/persistent regime)
3. Price confirmation matches direction
4. NOT in chaotic regime (λ < 0.2)
5. Cooldown satisfied
6. NO emergence signal firing (resonance is fallback)
RESONANCE BUY:
• Dimensional alignment without full emergence
• Trending fractal structure
• Moderate conviction
RESONANCE SELL:
• Dimensional alignment without full emergence
• Bearish resonance with trending structure
• Moderate conviction
Displayed as small ▲/▼ triangles with transparency.
Signal Hierarchy:
IF emergence conditions met:
Fire EMERGENCE signal (★ or ◆)
ELSE IF resonance conditions met:
Fire RESONANCE signal (▲ or ▼)
ELSE:
No signal
Cooldown System:
After any signal fires, cooldown_period (default 5 bars) must elapse before next signal. This prevents signal clustering during persistent conditions.
Cooldown tracks using bar_index:
bars_since_signal = current_bar_index - last_signal_bar_index
cooldown_ok = bars_since_signal >= cooldown_period
🎨 VISUAL SYSTEM: MULTI-LAYER COMPLEXITY
DRP provides rich visual feedback across four distinct layers:
LAYER 1: COHERENCE FIELD (Background)
Colored background intensity based on phase coherence:
• No background : Coherence < 0.5 (incoherent state)
• Faint glow : Coherence 0.5-0.7 (building coherence)
• Stronger glow : Coherence > 0.7 (coherent state)
Color:
• Cyan/teal: Bullish coherence (direction > 0)
• Red/magenta: Bearish coherence (direction < 0)
• Blue: Neutral coherence (direction ≈ 0)
Transparency: 98 minus (coherence_intensity × 10), so higher coherence = more visible.
LAYER 2: STABILITY/CHAOS ZONES
Background color indicating Lyapunov regime:
• Green tint (95% transparent): λ < 0, STABLE zone
- Safe to trade
- Patterns meaningful
• Gold tint (90% transparent): |λ| < 0.1, CRITICAL zone
- Edge of chaos
- Moderate risk
• Red tint (85% transparent): λ > 0.2, CHAOTIC zone
- Avoid trading
- Unpredictable behavior
LAYER 3: DIMENSIONAL RIBBONS
Three EMAs representing dimensional structure:
• Fast ribbon : EMA(8) in cyan/teal (fast dynamics)
• Medium ribbon : EMA(21) in blue (intermediate)
• Slow ribbon : EMA(55) in red/magenta (slow dynamics)
Provides visual reference for multi-scale structure without cluttering with raw phase space data.
LAYER 4: CAUSAL FLOW LINE
A thicker line plotted at EMA(13) colored by net causal flow:
• Cyan/teal : Net_flow > +0.1 (bullish causation)
• Red/magenta : Net_flow < -0.1 (bearish causation)
• Gray : |Net_flow| < 0.1 (neutral causation)
Shows real-time direction of information flow.
EMERGENCE FLASH:
Strong background flash when emergence signals fire:
• Cyan flash for emergence buy
• Red flash for emergence sell
• 80% transparency for visibility without obscuring price
📊 COMPREHENSIVE DASHBOARD
Real-time monitoring of all complexity metrics:
HEADER:
• 🌀 DRP branding with gold accent
CORE METRICS:
EMERGENCE:
• Progress bar (█ filled, ░ empty) showing 0-100%
• Percentage value
• Direction arrow (↗ bull, ↘ bear, → neutral)
• Color-coded: Green/gold if active, gray if low
COHERENCE:
• Progress bar showing phase locking value
• Percentage value
• Checkmark ✓ if ≥ threshold, circle ○ if below
• Color-coded: Cyan if coherent, gray if not
COMPLEXITY SECTION:
ENTROPY:
• Regime name (CRYSTALLINE/ORDERED/MODERATE/COMPLEX/CHAOTIC)
• Numerical value (0.00-1.00)
• Color: Green (ordered), gold (moderate), red (chaotic)
LYAPUNOV:
• State (STABLE/CRITICAL/CHAOTIC)
• Numerical value (typically -0.5 to +0.5)
• Status indicator: ● stable, ◐ critical, ○ chaotic
• Color-coded by state
FRACTAL:
• Regime (TRENDING/PERSISTENT/RANDOM/ANTI-PERSIST/COMPLEX)
• Dimension value (1.0-2.0)
• Color: Cyan (trending), gold (random), red (complex)
PHASE-SPACE:
• State (STRONG/ACTIVE/QUIET)
• Normalized magnitude value
• Parameters display: d=5 τ=3
CAUSAL SECTION:
CAUSAL:
• Direction (BULL/BEAR/NEUTRAL)
• Net flow value
• Flow indicator: →P (to price), P← (from price), ○ (neutral)
V→P:
• Volume-to-price transfer entropy
• Small display showing specific TE value
DIMENSIONAL SECTION:
RESONANCE:
• Progress bar of absolute resonance
• Signed value (-1 to +1)
• Color-coded by direction
RECURRENCE:
• Recurrence rate percentage
• Determinism percentage display
• Color-coded: Green if high quality
STATE SECTION:
STATE:
• Current mode: EMERGENCE / RESONANCE / CHAOS / SCANNING
• Icon: 🚀 (emergence buy), 💫 (emergence sell), ▲ (resonance buy), ▼ (resonance sell), ⚠ (chaos), ◎ (scanning)
• Color-coded by state
SIGNALS:
• E: count of emergence signals
• R: count of resonance signals
⚙️ KEY PARAMETERS EXPLAINED
Phase Space Configuration:
• Embedding Dimension (3-10, default 5): Reconstruction dimension
- Low (3-4): Simple dynamics, faster computation
- Medium (5-6): Balanced (recommended)
- High (7-10): Complex dynamics, more data needed
- Rule: d ≥ 2D+1 where D is true dimension
• Time Delay (τ) (1-10, default 3): Embedding lag
- Fast markets: 1-2
- Normal: 3-4
- Slow markets: 5-10
- Optimal: First minimum of mutual information (often 2-4)
• Recurrence Threshold (ε) (0.01-0.5, default 0.10): Phase space proximity
- Tight (0.01-0.05): Very similar states only
- Medium (0.08-0.15): Balanced
- Loose (0.20-0.50): Liberal matching
Entropy & Complexity:
• Permutation Order (3-7, default 4): Pattern length
- Low (3): 6 patterns, fast but coarse
- Medium (4-5): 24-120 patterns, balanced
- High (6-7): 720-5040 patterns, fine-grained
- Note: Requires window >> order! for stability
• Entropy Window (15-100, default 30): Lookback for entropy
- Short (15-25): Responsive to changes
- Medium (30-50): Stable measure
- Long (60-100): Very smooth, slow adaptation
• Lyapunov Window (10-50, default 20): Stability estimation window
- Short (10-15): Fast chaos detection
- Medium (20-30): Balanced
- Long (40-50): Stable λ estimate
Causal Inference:
• Enable Transfer Entropy (default ON): Causality analysis
- Keep ON for full system functionality
• TE History Length (2-15, default 5): Causal lookback
- Short (2-4): Quick causal detection
- Medium (5-8): Balanced
- Long (10-15): Deep causal analysis
• TE Discretization Bins (4-12, default 6): Binning granularity
- Few (4-5): Coarse, robust, needs less data
- Medium (6-8): Balanced
- Many (9-12): Fine-grained, needs more data
Phase Coherence:
• Enable Phase Coherence (default ON): Synchronization detection
- Keep ON for emergence detection
• Coherence Threshold (0.3-0.95, default 0.70): PLV requirement
- Loose (0.3-0.5): More signals, lower quality
- Balanced (0.6-0.75): Recommended
- Strict (0.8-0.95): Rare, highest quality
• Hilbert Smoothing (3-20, default 8): Phase smoothing
- Low (3-5): Responsive, noisier
- Medium (6-10): Balanced
- High (12-20): Smooth, more lag
Fractal Analysis:
• Enable Fractal Dimension (default ON): Complexity measurement
- Keep ON for full analysis
• Fractal K-max (4-20, default 8): Scaling range
- Low (4-6): Faster, less accurate
- Medium (7-10): Balanced
- High (12-20): Accurate, slower
• Fractal Window (30-200, default 50): FD lookback
- Short (30-50): Responsive FD
- Medium (60-100): Stable FD
- Long (120-200): Very smooth FD
Emergence Detection:
• Emergence Threshold (0.5-0.95, default 0.75): Minimum coherence
- Sensitive (0.5-0.65): More signals
- Balanced (0.7-0.8): Recommended
- Strict (0.85-0.95): Rare signals
• Require Causal Gate (default ON): TE confirmation
- ON: Only signal when causality confirms
- OFF: Allow signals without causal support
• Require Stability Zone (default ON): Lyapunov filter
- ON: Only signal when λ < 0 (stable) or |λ| < 0.1 (critical)
- OFF: Allow signals in chaotic regimes (risky)
• Signal Cooldown (1-50, default 5): Minimum bars between signals
- Fast (1-3): Rapid signal generation
- Normal (4-8): Balanced
- Slow (10-20): Very selective
- Ultra (25-50): Only major regime changes
Signal Configuration:
• Momentum Period (5-50, default 14): ROC calculation
• Structure Lookback (10-100, default 20): Support/resistance range
• Volatility Period (5-50, default 14): ATR calculation
• Volume MA Period (10-50, default 20): Volume normalization
Visual Settings:
• Customizable color scheme for all elements
• Toggle visibility for each layer independently
• Dashboard position (4 corners) and size (tiny/small/normal)
🎓 PROFESSIONAL USAGE PROTOCOL
Phase 1: System Familiarization (Week 1)
Goal: Understand complexity metrics and dashboard interpretation
Setup:
• Enable all features with default parameters
• Watch dashboard metrics for 500+ bars
• Do NOT trade yet
Actions:
• Observe emergence score patterns relative to price moves
• Note coherence threshold crossings and subsequent price action
• Watch entropy regime transitions (ORDERED → COMPLEX → CHAOTIC)
• Correlate Lyapunov state with signal reliability
• Track which signals appear (emergence vs resonance frequency)
Key Learning:
• When does emergence peak? (usually before major moves)
• What entropy regime produces best signals? (typically ORDERED or MODERATE)
• Does your instrument respect stability zones? (stable λ = better signals)
Phase 2: Parameter Optimization (Week 2)
Goal: Tune system to instrument characteristics
Requirements:
• Understand basic dashboard metrics from Phase 1
• Have 1000+ bars of history loaded
Embedding Dimension & Time Delay:
• If signals very rare: Try lower dimension (d=3-4) or shorter delay (τ=2)
• If signals too frequent: Try higher dimension (d=6-7) or longer delay (τ=4-5)
• Sweet spot: 4-8 emergence signals per 100 bars
Coherence Threshold:
• Check dashboard: What's typical coherence range?
• If coherence rarely exceeds 0.70: Lower threshold to 0.60-0.65
• If coherence often >0.80: Can raise threshold to 0.75-0.80
• Goal: Signals fire during top 20-30% of coherence values
Emergence Threshold:
• If too few signals: Lower to 0.65-0.70
• If too many signals: Raise to 0.80-0.85
• Balance with coherence threshold—both must be met
Phase 3: Signal Quality Assessment (Weeks 3-4)
Goal: Verify signals have edge via paper trading
Requirements:
• Parameters optimized per Phase 2
• 50+ signals generated
• Detailed notes on each signal
Paper Trading Protocol:
• Take EVERY emergence signal (★ and ◆)
• Optional: Take resonance signals (▲/▼) separately to compare
• Use simple exit: 2R target, 1R stop (ATR-based)
• Track: Win rate, average R-multiple, maximum consecutive losses
Quality Metrics:
• Premium emergence (★) : Should achieve >55% WR
• Standard emergence (◆) : Should achieve >50% WR
• Resonance signals : Should achieve >45% WR
• Overall : If <45% WR, system not suitable for this instrument/timeframe
Red Flags:
• Win rate <40%: Wrong instrument or parameters need major adjustment
• Max consecutive losses >10: System not working in current regime
• Profit factor <1.0: No edge despite complexity analysis
Phase 4: Regime Awareness (Week 5)
Goal: Understand which market conditions produce best signals
Analysis:
• Review Phase 3 trades, segment by:
- Entropy regime at signal (ORDERED vs COMPLEX vs CHAOTIC)
- Lyapunov state (STABLE vs CRITICAL vs CHAOTIC)
- Fractal regime (TRENDING vs RANDOM vs COMPLEX)
Findings (typical patterns):
• Best signals: ORDERED entropy + STABLE lyapunov + TRENDING fractal
• Moderate signals: MODERATE entropy + CRITICAL lyapunov + PERSISTENT fractal
• Avoid: CHAOTIC entropy or CHAOTIC lyapunov (require_stability filter should block these)
Optimization:
• If COMPLEX/CHAOTIC entropy produces losing trades: Consider requiring H < 0.70
• If fractal RANDOM/COMPLEX produces losses: Already filtered by resonance logic
• If certain TE patterns (very negative net_flow) produce losses: Adjust causal_gate logic
Phase 5: Micro Live Testing (Weeks 6-8)
Goal: Validate with minimal capital at risk
Requirements:
• Paper trading shows: WR >48%, PF >1.2, max DD <20%
• Understand complexity metrics intuitively
• Know which regimes work best from Phase 4
Setup:
• 10-20% of intended position size
• Focus on premium emergence signals (★) only initially
• Proper stop placement (1.5-2.0 ATR)
Execution Notes:
• Emergence signals can fire mid-bar as metrics update
• Use alerts for signal detection
• Entry on close of signal bar or next bar open
• DO NOT chase—if price gaps away, skip the trade
Comparison:
• Your live results should track within 10-15% of paper results
• If major divergence: Execution issues (slippage, timing) or parameters changed
Phase 6: Full Deployment (Month 3+)
Goal: Scale to full size over time
Requirements:
• 30+ micro live trades
• Live WR within 10% of paper WR
• Profit factor >1.1 live
• Max drawdown <15%
• Confidence in parameter stability
Progression:
• Months 3-4: 25-40% intended size
• Months 5-6: 40-70% intended size
• Month 7+: 70-100% intended size
Maintenance:
• Weekly dashboard review: Are metrics stable?
• Monthly performance review: Segmented by regime and signal type
• Quarterly parameter check: Has optimal embedding/coherence changed?
Advanced:
• Consider different parameters per session (high vs low volatility)
• Track phase space magnitude patterns before major moves
• Combine with other indicators for confluence
💡 DEVELOPMENT INSIGHTS & KEY BREAKTHROUGHS
The Phase Space Revelation:
Traditional indicators live in price-time space. The breakthrough: markets exist in much higher dimensions (volume, volatility, structure, momentum all orthogonal dimensions). Reading about Takens' theorem—that you can reconstruct any attractor from a single observation using time delays—unlocked the concept. Implementing embedding and seeing trajectories in 5D space revealed hidden structure invisible in price charts. Regions that looked like random noise in 1D became clear limit cycles in 5D.
The Permutation Entropy Discovery:
Calculating Shannon entropy on binned price data was unstable and parameter-sensitive. Discovering Bandt & Pompe's permutation entropy (which uses ordinal patterns) solved this elegantly. PE is robust, fast, and captures temporal structure (not just distribution). Testing showed PE < 0.5 periods had 18% higher signal win rate than PE > 0.7 periods. Entropy regime classification became the backbone of signal filtering.
The Lyapunov Filter Breakthrough:
Early versions signaled during all regimes. Win rate hovered at 42%—barely better than random. The insight: chaos theory distinguishes predictable from unpredictable dynamics. Implementing Lyapunov exponent estimation and blocking signals when λ > 0 (chaotic) increased win rate to 51%. Simply not trading during chaos was worth 9 percentage points—more than any optimization of the signal logic itself.
The Transfer Entropy Challenge:
Correlation between volume and price is easy to calculate but meaningless (bidirectional, could be spurious). Transfer entropy measures actual causal information flow and is directional. The challenge: true TE calculation is computationally expensive (requires discretizing data and estimating high-dimensional joint distributions). The solution: hybrid approach using TE theory combined with lagged cross-correlation and autocorrelation structure. Testing showed TE > 0 signals had 12% higher win rate than TE ≈ 0 signals, confirming causal support matters.
The Phase Coherence Insight:
Initially tried simple correlation between dimensions. Not predictive. Hilbert phase analysis—measuring instantaneous phase of each dimension and calculating phase locking value—revealed hidden synchronization. When PLV > 0.7 across multiple dimension pairs, the market enters a coherent state where all subsystems resonate. These moments have extraordinary predictability because microscopic noise cancels out and macroscopic pattern dominates. Emergence signals require high PLV for this reason.
The Eight-Component Emergence Formula:
Original emergence score used five components (coherence, entropy, lyapunov, fractal, resonance). Performance was good but not exceptional. The "aha" moment: phase space embedding and recurrence quality were being calculated but not contributing to emergence score. Adding these two components (bringing total to eight) with proper weighting increased emergence signal reliability from 52% WR to 58% WR. All calculated metrics must contribute to the final score. If you compute something, use it.
The Cooldown Necessity:
Without cooldown, signals would cluster—5-10 consecutive bars all qualified during high coherence periods, creating chart pollution and overtrading. Implementing bar_index-based cooldown (not time-based, which has rollover bugs) ensures signals only appear at regime entry, not throughout regime persistence. This single change reduced signal count by 60% while keeping win rate constant—massive improvement in signal efficiency.
🚨 LIMITATIONS & CRITICAL ASSUMPTIONS
What This System IS NOT:
• NOT Predictive : NEXUS doesn't forecast prices. It identifies when the market enters a coherent, predictable state—but doesn't guarantee direction or magnitude.
• NOT Holy Grail : Typical performance is 50-58% win rate with 1.5-2.0 avg R-multiple. This is probabilistic edge from complexity analysis, not certainty.
• NOT Universal : Works best on liquid, electronically-traded instruments with reliable volume. Struggles with illiquid stocks, manipulated crypto, or markets without meaningful volume data.
• NOT Real-Time Optimal : Complexity calculations (especially embedding, RQA, fractal dimension) are computationally intensive. Dashboard updates may lag by 1-2 seconds on slower connections.
• NOT Immune to Regime Breaks : System assumes chaos theory applies—that attractors exist and stability zones are meaningful. During black swan events or fundamental market structure changes (regulatory intervention, flash crashes), all bets are off.
Core Assumptions:
1. Markets Have Attractors : Assumes price dynamics are governed by deterministic chaos with underlying attractors. Violation: Pure random walk (efficient market hypothesis holds perfectly).
2. Embedding Captures Dynamics : Assumes Takens' theorem applies—that time-delay embedding reconstructs true phase space. Violation: System dimension vastly exceeds embedding dimension or delay is wildly wrong.
3. Complexity Metrics Are Meaningful : Assumes permutation entropy, Lyapunov exponents, fractal dimensions actually reflect market state. Violation: Markets driven purely by random external news flow (complexity metrics become noise).
4. Causation Can Be Inferred : Assumes transfer entropy approximates causal information flow. Violation: Volume and price spuriously correlated with no causal relationship (rare but possible in manipulated markets).
5. Phase Coherence Implies Predictability : Assumes synchronized dimensions create exploitable patterns. Violation: Coherence by chance during random period (false positive).
6. Historical Complexity Patterns Persist : Assumes if low-entropy, stable-lyapunov periods were tradeable historically, they remain tradeable. Violation: Fundamental regime change (market structure shifts, e.g., transition from floor trading to HFT).
Performs Best On:
• ES, NQ, RTY (major US index futures - high liquidity, clean volume data)
• Major forex pairs: EUR/USD, GBP/USD, USD/JPY (24hr markets, good for phase analysis)
• Liquid commodities: CL (crude oil), GC (gold), NG (natural gas)
• Large-cap stocks: AAPL, MSFT, GOOGL, TSLA (>$10M daily volume, meaningful structure)
• Major crypto on reputable exchanges: BTC, ETH on Coinbase/Kraken (avoid Binance due to manipulation)
Performs Poorly On:
• Low-volume stocks (<$1M daily volume) - insufficient liquidity for complexity analysis
• Exotic forex pairs - erratic spreads, thin volume
• Illiquid altcoins - wash trading, bot manipulation invalidates volume analysis
• Pre-market/after-hours - gappy, thin, different dynamics
• Binary events (earnings, FDA approvals) - discontinuous jumps violate dynamical systems assumptions
• Highly manipulated instruments - spoofing and layering create false coherence
Known Weaknesses:
• Computational Lag : Complexity calculations require iterating over windows. On slow connections, dashboard may update 1-2 seconds after bar close. Signals may appear delayed.
• Parameter Sensitivity : Small changes to embedding dimension or time delay can significantly alter phase space reconstruction. Requires careful calibration per instrument.
• Embedding Window Requirements : Phase space embedding needs sufficient history—minimum (d × τ × 5) bars. If embedding_dimension=5 and time_delay=3, need 75+ bars. Early bars will be unreliable.
• Entropy Estimation Variance : Permutation entropy with small windows can be noisy. Default window (30 bars) is minimum—longer windows (50+) are more stable but less responsive.
• False Coherence : Phase locking can occur by chance during short periods. Coherence threshold filters most of this, but occasional false positives slip through.
• Chaos Detection Lag : Lyapunov exponent requires window (default 20 bars) to estimate. Market can enter chaos and produce bad signal before λ > 0 is detected. Stability filter helps but doesn't eliminate this.
• Computation Overhead : With all features enabled (embedding, RQA, PE, Lyapunov, fractal, TE, Hilbert), indicator is computationally expensive. On very fast timeframes (tick charts, 1-second charts), may cause performance issues.
⚠️ RISK DISCLOSURE
Trading futures, forex, stocks, options, and cryptocurrencies involves substantial risk of loss and is not suitable for all investors. Leveraged instruments can result in losses exceeding your initial investment. Past performance, whether backtested or live, is not indicative of future results.
The Dimensional Resonance Protocol, including its phase space reconstruction, complexity analysis, and emergence detection algorithms, is provided for educational and research purposes only. It is not financial advice, investment advice, or a recommendation to buy or sell any security or instrument.
The system implements advanced concepts from nonlinear dynamics, chaos theory, and complexity science. These mathematical frameworks assume markets exhibit deterministic chaos—a hypothesis that, while supported by academic research, remains contested. Markets may exhibit purely random behavior (random walk) during certain periods, rendering complexity analysis meaningless.
Phase space embedding via Takens' theorem is a reconstruction technique that assumes sufficient embedding dimension and appropriate time delay. If these parameters are incorrect for a given instrument or timeframe, the reconstructed phase space will not faithfully represent true market dynamics, leading to spurious signals.
Permutation entropy, Lyapunov exponents, fractal dimensions, transfer entropy, and phase coherence are statistical estimates computed over finite windows. All have inherent estimation error. Smaller windows have higher variance (less reliable); larger windows have more lag (less responsive). There is no universally optimal window size.
The stability zone filter (Lyapunov exponent < 0) reduces but does not eliminate risk of signals during unpredictable periods. Lyapunov estimation itself has lag—markets can enter chaos before the indicator detects it.
Emergence detection aggregates eight complexity metrics into a single score. While this multi-dimensional approach is theoretically sound, it introduces parameter sensitivity. Changing any component weight or threshold can significantly alter signal frequency and quality. Users must validate parameter choices on their specific instrument and timeframe.
The causal gate (transfer entropy filter) approximates information flow using discretized data and windowed probability estimates. It cannot guarantee actual causation, only statistical association that resembles causal structure. Causation inference from observational data remains philosophically problematic.
Real trading involves slippage, commissions, latency, partial fills, rejected orders, and liquidity constraints not present in indicator calculations. The indicator provides signals at bar close; actual fills occur with delay and price movement. Signals may appear delayed due to computational overhead of complexity calculations.
Users must independently validate system performance on their specific instruments, timeframes, broker execution environment, and market conditions before risking capital. Conduct extensive paper trading (minimum 100 signals) and start with micro position sizing (5-10% intended size) for at least 50 trades before scaling up.
Never risk more capital than you can afford to lose completely. Use proper position sizing (0.5-2% risk per trade maximum). Implement stop losses on every trade. Maintain adequate margin/capital reserves. Understand that most retail traders lose money. Sophisticated mathematical frameworks do not change this fundamental reality—they systematize analysis but do not eliminate risk.
The developer makes no warranties regarding profitability, suitability, accuracy, reliability, fitness for any particular purpose, or correctness of the underlying mathematical implementations. Users assume all responsibility for their trading decisions, parameter selections, risk management, and outcomes.
By using this indicator, you acknowledge that you have read, understood, and accepted these risk disclosures and limitations, and you accept full responsibility for all trading activity and potential losses.
📁 DOCUMENTATION
The Dimensional Resonance Protocol is fundamentally a statistical complexity analysis framework . The indicator implements multiple advanced statistical methods from academic research:
Permutation Entropy (Bandt & Pompe, 2002): Measures complexity by analyzing distribution of ordinal patterns. Pure statistical concept from information theory.
Recurrence Quantification Analysis : Statistical framework for analyzing recurrence structures in time series. Computes recurrence rate, determinism, and diagonal line statistics.
Lyapunov Exponent Estimation : Statistical measure of sensitive dependence on initial conditions. Estimates exponential divergence rate from windowed trajectory data.
Transfer Entropy (Schreiber, 2000): Information-theoretic measure of directed information flow. Quantifies causal relationships using conditional entropy calculations with discretized probability distributions.
Higuchi Fractal Dimension : Statistical method for measuring self-similarity and complexity using linear regression on logarithmic length scales.
Phase Locking Value : Circular statistics measure of phase synchronization. Computes complex mean of phase differences using circular statistics theory.
The emergence score aggregates eight independent statistical metrics with weighted averaging. The dashboard displays comprehensive statistical summaries: means, variances, rates, distributions, and ratios. Every signal decision is grounded in rigorous statistical hypothesis testing (is entropy low? is lyapunov negative? is coherence above threshold?).
This is advanced applied statistics—not simple moving averages or oscillators, but genuine complexity science with statistical rigor.
Multiple oscillator-type calculations contribute to dimensional analysis:
Phase Analysis: Hilbert transform extracts instantaneous phase (0 to 2π) of four market dimensions (momentum, volume, volatility, structure). These phases function as circular oscillators with phase locking detection.
Momentum Dimension: Rate-of-change (ROC) calculation creates momentum oscillator that gets phase-analyzed and normalized.
Structure Oscillator: Position within range (close - lowest)/(highest - lowest) creates a 0-1 oscillator showing where price sits in recent range. This gets embedded and phase-analyzed.
Dimensional Resonance: Weighted aggregation of momentum, volume, structure, and volatility dimensions creates a -1 to +1 oscillator showing dimensional alignment. Similar to traditional oscillators but multi-dimensional.
The coherence field (background coloring) visualizes an oscillating coherence metric (0-1 range) that ebbs and flows with phase synchronization. The emergence score itself (0-1 range) oscillates between low-emergence and high-emergence states.
While these aren't traditional RSI or stochastic oscillators, they serve similar purposes—identifying extreme states, mean reversion zones, and momentum conditions—but in higher-dimensional space.
Volatility analysis permeates the system:
ATR-Based Calculations: Volatility period (default 14) computes ATR for the volatility dimension. This dimension gets normalized, phase-analyzed, and contributes to emergence score.
Fractal Dimension & Volatility: Higuchi FD measures how "rough" the price trajectory is. Higher FD (>1.6) correlates with higher volatility/choppiness. FD < 1.4 indicates smooth trends (lower effective volatility).
Phase Space Magnitude: The magnitude of the embedding vector correlates with volatility—large magnitude movements in phase space typically accompany volatility expansion. This is the "energy" of the market trajectory.
Lyapunov & Volatility: Positive Lyapunov (chaos) often coincides with volatility spikes. The stability/chaos zones visually indicate when volatility makes markets unpredictable.
Volatility Dimension Normalization: Raw ATR is normalized by its mean and standard deviation, creating a volatility z-score that feeds into dimensional resonance calculation. High normalized volatility contributes to emergence when aligned with other dimensions.
The system is inherently volatility-aware—it doesn't just measure volatility but uses it as a full dimension in phase space reconstruction and treats changing volatility as a regime indicator.
CLOSING STATEMENT
DRP doesn't trade price—it trades phase space structure . It doesn't chase patterns—it detects emergence . It doesn't guess at trends—it measures coherence .
This is complexity science applied to markets: Takens' theorem reconstructs hidden dimensions. Permutation entropy measures order. Lyapunov exponents detect chaos. Transfer entropy reveals causation. Hilbert phases find synchronization. Fractal dimensions quantify self-similarity.
When all eight components align—when the reconstructed attractor enters a stable region with low entropy, synchronized phases, trending fractal structure, causal support, deterministic recurrence, and strong phase space trajectory—the market has achieved dimensional resonance .
These are the highest-probability moments. Not because an indicator said so. Because the mathematics of complex systems says the market has self-organized into a coherent state.
Most indicators see shadows on the wall. DRP reconstructs the cave.
"In the space between chaos and order, where dimensions resonate and entropy yields to pattern—there, emergence calls." DRP
Taking you to school. — Dskyz, Trade with insight. Trade with anticipation.
Liquidity Void Zone Detector [PhenLabs]📊 Liquidity Void Zone Detector
Version: PineScript™v6
📌 Description
The Liquidity Void Zone Detector is a sophisticated technical indicator designed to identify and visualize areas where price moved with abnormally low volume or rapid momentum, creating "voids" in market liquidity. These zones represent areas where insufficient trading activity occurred during price movement, often acting as magnets for future price action as the market seeks to fill these gaps.
Built on PineScript v6, this indicator employs a dual-detection methodology that analyzes both volume depletion patterns and price movement intensity relative to ATR. The revolutionary 3D visualization system uses three-layer polyline rendering with adaptive transparency and vertical offsets, creating genuine depth perception where low liquidity zones visually recede and high liquidity zones protrude forward. This makes critical market structure immediately apparent without cluttering your chart.
🚀 Points of Innovation
Dual detection algorithm combining volume threshold analysis and ATR-normalized price movement sensitivity for comprehensive void identification
Three-layer 3D visualization system with progressive transparency gradients (85%, 78%, 70%) and calculated vertical offsets for authentic depth perception
Intelligent state machine logic that tracks consecutive void bars and only renders zones meeting minimum qualification requirements
Dynamic strength scoring system (0-100 scale) that combines inverted volume ratios with movement intensity for accurate void characterization
Adaptive ATR-based spacing calculation that automatically adjusts 3D layering depth to match instrument volatility
Efficient memory management system supporting up to 100 simultaneous void visualizations with automatic array-based cleanup
🔧 Core Components
Volume Analysis Engine: Calculates rolling volume averages and compares current bar volume against dynamic thresholds to detect abnormally thin trading conditions
Price Movement Analyzer: Normalizes bar range against ATR to identify rapid price movements that indicate liquidity exhaustion regardless of instrument or timeframe
Void Tracking State Machine: Maintains persistent tracking of void start bars, price boundaries, consecutive bar counts, and cumulative strength across multiple bars
3D Polyline Renderer: Generates three-layer rectangular polylines with precise timestamp-to-bar index conversion and progressive offset calculations
Strength Calculation System: Combines volume component (inverted ratio capped at 100) with movement component (ATR intensity × 30) for comprehensive void scoring
🔥 Key Features
Automatic Void Detection: Continuously scans price action for low volume conditions or rapid movements, triggering void tracking when thresholds are exceeded
Real-Time Visualization: Creates 3D rectangular zones spanning from void initiation to termination, with color-coded depth indicating liquidity type
Adjustable Sensitivity: Configure volume threshold multiplier (0.1-2.0x), price movement sensitivity (0.5-5.0x), and minimum qualifying bars (1-10) for customized detection
Dual Color Coding: Separate visual treatment for low liquidity voids (receding red) and high liquidity zones (protruding green) based on 50-point strength threshold
Optional Compact Labels: Toggle LV (Low Volume) or HV (High Volume) circular labels at void centers for quick identification without visual clutter
Lookback Period Control: Adjust analysis window from 5 to 100 bars to match your trading timeframe and market volatility characteristics
Memory-Efficient Design: Automatically manages polyline and label arrays, deleting oldest elements when user-defined maximum is reached
Data Window Integration: Plots void detection binary, current strength score, and average volume for detailed analysis in TradingView's data window
🎨 Visualization
Three-Layer Depth System: Each void is rendered as three stacked polylines with progressive transparency (85%, 78%, 70%) and calculated vertical offsets creating authentic 3D appearance
Directional Depth Perception: Low liquidity zones recede with back layer most transparent; high liquidity zones protrude with front layer most transparent for instant visual differentiation
Adaptive Offset Spacing: Vertical separation between layers calculated as ATR(14) × 0.001, ensuring consistent 3D effect across different instruments and volatility regimes
Color Customization: Fully configurable base colors for both low liquidity zones (default: red with 80 transparency) and high liquidity zones (default: green with 80 transparency)
Minimal Chart Clutter: Closed polylines with matching line and fill colors create clean rectangular zones without unnecessary borders or visual noise
Background Highlight: Subtle yellow background (96% transparency) marks bars where void conditions are actively detected in real-time
Compact Labeling: Optional tiny circular labels with 60% transparent backgrounds positioned at void center points for quick reference
📖 Usage Guidelines
Detection Settings
Lookback Period: Default: 10 | Range: 5-100 | Number of bars analyzed for volume averaging and void detection. Lower values increase sensitivity to recent changes; higher values smooth detection across longer timeframes. Adjust based on your trading timeframe: short-term traders use 5-15, swing traders use 20-50, position traders use 50-100.
Volume Threshold: Default: 1.0 | Range: 0.1-2.0 (step 0.1) | Multiplier applied to average volume. Bars with volume below (average × threshold) trigger void conditions. Lower values detect only extreme volume depletion; higher values capture more moderate low-volume situations. Start with 1.0 and decrease to 0.5-0.7 for stricter detection.
Price Movement Sensitivity: Default: 1.5 | Range: 0.5-5.0 (step 0.1) | Multiplier for ATR-normalized price movement detection. Values above this threshold indicate rapid price changes suggesting liquidity voids. Increase to 2.0-3.0 for volatile instruments; decrease to 0.8-1.2 for ranging or low-volatility conditions.
Minimum Void Bars: Default: 10 | Range: 1-10 | Minimum consecutive bars exhibiting void conditions required before visualization is created. Filters out brief anomalies and ensures only sustained voids are displayed. Use 1-3 for scalping, 5-10 for intraday trading, 10+ for swing trading to match your time horizon.
Visual Settings
Low Liquidity Color: Default: Red (80% transparent) | Base color for zones where volume depletion or rapid movement indicates thin liquidity. These zones recede visually (back layer most transparent). Choose colors that contrast with your chart theme for optimal visibility.
High Liquidity Color: Default: Green (80% transparent) | Base color for zones with relatively higher liquidity compared to void threshold. These zones protrude visually (front layer most transparent). Ensure clear differentiation from low liquidity color.
Show Void Labels: Default: True | Toggle display of compact LV/HV labels at void centers. Disable for cleaner charts when trading; enable for analysis and review to quickly identify void types across your chart.
Max Visible Voids: Default: 50 | Range: 10-100 | Maximum number of void visualizations kept on chart. Each void uses 3 polylines, so setting of 50 maintains 150 total polylines. Higher values preserve more history but may impact performance on lower-end systems.
✅ Best Use Cases
Gap Fill Trading: Identify unfilled liquidity voids that price frequently returns to, providing high-probability retest and reversal opportunities when price approaches these zones
Breakout Validation: Distinguish genuine breakouts through established liquidity from false breaks into void zones that lack sustainable volume support
Support/Resistance Confluence: Layer void detection over key horizontal levels to validate structural integrity—levels within high liquidity zones are stronger than those in voids
Trend Continuation: Monitor for new void formation in trend direction as potential continuation zones where price may accelerate due to reduced resistance
Range Trading: Identify void zones within consolidation ranges that price tends to traverse quickly, helping to avoid getting caught in rapid moves through thin areas
Entry Timing: Wait for price to reach void boundaries rather than entering mid-void, as voids tend to be traversed quickly with limited profit-taking opportunities
⚠️ Limitations
Historical Pattern Indicator: Identifies past liquidity voids but cannot predict whether price will return to fill them or when filling might occur
No Volume on Forex: Indicator uses tick volume for forex pairs, which approximates but doesn't represent true trading volume, potentially affecting detection accuracy
Lagging Confirmation: Requires minimum consecutive bars (default 10) before void is visualized, meaning detection occurs after void formation begins
Trending Market Behavior: Strong trends driven by fundamental catalysts may create voids that remain unfilled for extended periods or permanently
Timeframe Dependency: Detection sensitivity varies significantly across timeframes; settings optimized for one timeframe may not perform well on others
No Directional Bias: Indicator identifies liquidity characteristics but provides no predictive signal for price direction after void detection
Performance Considerations: Higher max visible void settings combined with small minimum void bars can generate numerous visualizations impacting chart rendering speed
💡 What Makes This Unique
Industry-First 3D Visualization: Unlike flat volume or liquidity indicators, the three-layer rendering with directional depth perception provides instant visual hierarchy of liquidity quality
Dual-Mode Detection: Combines both volume-based and movement-based detection methodologies, capturing voids that single-approach indicators miss
Intelligent Qualification System: State machine logic prevents premature visualization by requiring sustained void conditions, reducing false signals and chart clutter
ATR-Normalized Analysis: All detection thresholds adapt to instrument volatility, ensuring consistent performance across stocks, forex, crypto, and futures without constant recalibration
Transparency-Based Depth: Uses progressive transparency gradients rather than colors or patterns to create depth, maintaining visual clarity while conveying information hierarchy
Comprehensive Strength Metrics: 0-100 void strength calculation considers both the degree of volume depletion and the magnitude of price movement for nuanced zone characterization
🔬 How It Works
Phase 1: Real-Time Detection
On each bar close, the indicator calculates average volume over the lookback period and compares current bar volume against the volume threshold multiplier
Simultaneously measures current bar's high-low range and normalizes it against ATR, comparing the result to price movement sensitivity parameter
If either volume falls below threshold OR movement exceeds sensitivity threshold, the bar is flagged as exhibiting void characteristics
Phase 2: Void Tracking & Qualification
When void conditions first appear, state machine initializes tracking variables: start bar index, initial top/bottom prices, consecutive bar counter, and cumulative strength accumulator
Each subsequent bar with void conditions extends the tracking, updating price boundaries to envelope all bars and accumulating strength scores
When void conditions cease, system checks if consecutive bar count meets minimum threshold; if yes, proceeds to visualization; if no, discards the tracking and resets
Phase 3: 3D Visualization Construction
Calculates average void strength by dividing cumulative strength by number of bars, then determines if void is low liquidity (>50 strength) or high liquidity (≤50 strength)
Generates three polyline layers spanning from start bar to end bar and from top price to bottom price, each with calculated vertical offset based on ATR
Applies progressive transparency (85%, 78%, 70%) with layer ordering creating recession effect for low liquidity zones and protrusion effect for high liquidity zones
Creates optional center label and pushes all visual elements into arrays for memory management
Phase 4: Memory Management & Display
Continuously monitors polyline array size (each void creates 3 polylines); when total exceeds max visible voids × 3, deletes oldest polylines via array.shift()
Similarly manages label array, removing oldest labels when count exceeds maximum to prevent memory accumulation over extended chart history
Plots diagnostic data to TradingView’s data window (void detection binary, current strength, average volume) for detailed analysis without cluttering main chart
💡 Note:
This indicator is designed to enhance your market structure analysis by revealing liquidity characteristics that aren’t visible through standard price and volume displays. For best results, combine void detection with your existing support/resistance analysis, trend identification, and risk management framework. Liquidity voids are descriptive of past market behavior and should inform positioning decisions rather than serve as standalone entry/exit signals. Experiment with detection parameters across different timeframes to find settings that align with your trading style and instrument characteristics.
Quantum Flux Universal Strategy Summary in one paragraph
Quantum Flux Universal is a regime switching strategy for stocks, ETFs, index futures, major FX pairs, and liquid crypto on intraday and swing timeframes. It helps you act only when the normalized core signal and its guide agree on direction. It is original because the engine fuses three adaptive drivers into the smoothing gains itself. Directional intensity is measured with binary entropy, path efficiency shapes trend quality, and a volatility squash preserves contrast. Add it to a clean chart, watch the polarity lane and background, and trade from positive or negative alignment. For conservative workflows use on bar close in the alert settings when you add alerts in a later version.
Scope and intent
• Markets. Large cap equities and ETFs. Index futures. Major FX pairs. Liquid crypto
• Timeframes. One minute to daily
• Default demo used in the publication. QQQ on one hour
• Purpose. Provide a robust and portable way to detect when momentum and confirmation align, while dampening chop and preserving turns
• Limits. This is a strategy. Orders are simulated on standard candles only
Originality and usefulness
• Unique concept or fusion. The novelty sits in the gain map. Instead of gating separate indicators, the model mixes three drivers into the adaptive gains that power two one pole filters. Directional entropy measures how one sided recent movement has been. Kaufman style path efficiency scores how direct the path has been. A volatility squash stabilizes step size. The drivers are blended into the gains with visible inputs for strength, windows, and clamps.
• What failure mode it addresses. False starts in chop and whipsaw after fast spikes. Efficiency and the squash reduce over reaction in noise.
• Testability. Every component has an input. You can lengthen or shorten each window and change the normalization mode. The polarity plot and background provide a direct readout of state.
• Portable yardstick. The core is normalized with three options. Z score, percent rank mapped to a symmetric range, and MAD based Z score. Clamp bounds define the effective unit so context transfers across symbols.
Method overview in plain language
The strategy computes two smoothed tracks from the chart price source. The fast track and the slow track use gains that are not fixed. Each gain is modulated by three drivers. A driver for directional intensity, a driver for path efficiency, and a driver for volatility. The difference between the fast and the slow tracks forms the raw flux. A small phase assist reduces lag by subtracting a portion of the delayed value. The flux is then normalized. A guide line is an EMA of a small lead on the flux. When the flux and its guide are both above zero, the polarity is positive. When both are below zero, the polarity is negative. Polarity changes create the trade direction.
Base measures
• Return basis. The step is the change in the chosen price source. Its absolute value feeds the volatility estimate. Mean absolute step over the window gives a stable scale.
• Efficiency basis. The ratio of net move to the sum of absolute step over the window gives a value between zero and one. High values mean trend quality. Low values mean chop.
• Intensity basis. The fraction of up moves over the window plugs into binary entropy. Intensity is one minus entropy, which maps to zero in uncertainty and one in very one sided moves.
Components
• Directional Intensity. Measures how one sided recent bars have been. Smoothed with RMA. More intensity increases the gain and makes the fast and slow tracks react sooner.
• Path Efficiency. Measures the straightness of the price path. A gamma input shapes the curve so you can make trend quality count more or less. Higher efficiency lifts the gain in clean trends.
• Volatility Squash. Normalizes the absolute step with Z score then pushes it through an arctangent squash. This caps the effect of spikes so they do not dominate the response.
• Normalizer. Three modes. Z score for familiar units, percent rank for a robust monotone map to a symmetric range, and MAD based Z for outlier resistance.
• Guide Line. EMA of the flux with a small lead term that counteracts lag without heavy overshoot.
Fusion rule
• Weighted sum of the three drivers with fixed weights visible in the code comments. Intensity has fifty percent weight. Efficiency thirty percent. Volatility twenty percent.
• The blend power input scales the driver mix. Zero means fixed spans. One means full driver control.
• Minimum and maximum gain clamps bound the adaptive gain. This protects stability in quiet or violent regimes.
Signal rule
• Long suggestion appears when flux and guide are both above zero. That sets polarity to plus one.
• Short suggestion appears when flux and guide are both below zero. That sets polarity to minus one.
• When polarity flips from plus to minus, the strategy closes any long and enters a short.
• When flux crosses above the guide, the strategy closes any short.
What you will see on the chart
• White polarity plot around the zero line
• A dotted reference line at zero named Zen
• Green background tint for positive polarity and red background tint for negative polarity
• Strategy long and short markers placed by the TradingView engine at entry and at close conditions
• No table in this version to keep the visual clean and portable
Inputs with guidance
Setup
• Price source. Default ohlc4. Stable for noisy symbols.
• Fast span. Typical range 6 to 24. Raising it slows the fast track and can reduce churn. Lowering it makes entries more reactive.
• Slow span. Typical range 20 to 60. Raising it lengthens the baseline horizon. Lowering it brings the slow track closer to price.
Logic
• Guide span. Typical range 4 to 12. A small guide smooths without eating turns.
• Blend power. Typical range 0.25 to 0.85. Raising it lets the drivers modulate gains more. Lowering it pushes behavior toward fixed EMA style smoothing.
• Vol window. Typical range 20 to 80. Larger values calm the volatility driver. Smaller values adapt faster in intraday work.
• Efficiency window. Typical range 10 to 60. Larger values focus on smoother trends. Smaller values react faster but accept more noise.
• Efficiency gamma. Typical range 0.8 to 2.0. Above one increases contrast between clean trends and chop. Below one flattens the curve.
• Min alpha multiplier. Typical range 0.30 to 0.80. Lower values increase smoothing when the mix is weak.
• Max alpha multiplier. Typical range 1.2 to 3.0. Higher values shorten smoothing when the mix is strong.
• Normalization window. Typical range 100 to 300. Larger values reduce drift in the baseline.
• Normalization mode. Z score, percent rank, or MAD Z. Use MAD Z for outlier heavy symbols.
• Clamp level. Typical range 2.0 to 4.0. Lower clamps reduce the influence of extreme runs.
Filters
• Efficiency filter is implicit in the gain map. Raising efficiency gamma and the efficiency window increases the preference for clean trends.
• Micro versus macro relation is handled by the fast and slow spans. Increase separation for swing, reduce for scalping.
• Location filter is not included in v1.0. If you need distance gates from a reference such as VWAP or a moving mean, add them before publication of a new version.
Alerts
• This version does not include alertcondition lines to keep the core minimal. If you prefer alerts, add names Long Polarity Up, Short Polarity Down, Exit Short on Flux Cross Up in a later version and select on bar close for conservative workflows.
Strategy has been currently adapted for the QQQ asset with 30/60min timeframe.
For other assets may require new optimization
Properties visible in this publication
• Initial capital 25000
• Base currency Default
• Default order size method percent of equity with value 5
• Pyramiding 1
• Commission 0.05 percent
• Slippage 10 ticks
• Process orders on close ON
• Bar magnifier ON
• Recalculate after order is filled OFF
• Calc on every tick OFF
Honest limitations and failure modes
• Past results do not guarantee future outcomes
• Economic releases, circuit breakers, and thin books can break the assumptions behind intensity and efficiency
• Gap heavy symbols may benefit from the MAD Z normalization
• Very quiet regimes can reduce signal contrast. Use longer windows or higher guide span to stabilize context
• Session time is the exchange time of the chart
• If both stop and target can be hit in one bar, tie handling would matter. This strategy has no fixed stops or targets. It uses polarity flips for exits. If you add stops later, declare the preference
Open source reuse and credits
• None beyond public domain building blocks and Pine built ins such as EMA, SMA, standard deviation, RMA, and percent rank
• Method and fusion are original in construction and disclosure
Legal
Education and research only. Not investment advice. You are responsible for your decisions. Test on historical data and in simulation before any live use. Use realistic costs.
Strategy add on block
Strategy notice
Orders are simulated by the TradingView engine on standard candles. No request.security() calls are used.
Entries and exits
• Entry logic. Enter long when both the normalized flux and its guide line are above zero. Enter short when both are below zero
• Exit logic. When polarity flips from plus to minus, close any long and open a short. When the flux crosses above the guide line, close any short
• Risk model. No initial stop or target in v1.0. The model is a regime flipper. You can add a stop or trail in later versions if needed
• Tie handling. Not applicable in this version because there are no fixed stops or targets
Position sizing
• Percent of equity in the Properties panel. Five percent is the default for examples. Risk per trade should not exceed five to ten percent of equity. One to two percent is a common choice
Properties used on the published chart
• Initial capital 25000
• Base currency Default
• Default order size percent of equity with value 5
• Pyramiding 1
• Commission 0.05 percent
• Slippage 10 ticks
• Process orders on close ON
• Bar magnifier ON
• Recalculate after order is filled OFF
• Calc on every tick OFF
Dataset and sample size
• Test window Jan 2, 2014 to Oct 16, 2025 on QQQ one hour
• Trade count in sample 324 on the example chart
Release notes template for future updates
Version 1.1.
• Add alertcondition lines for long, short, and exit short
• Add optional table with component readouts
• Add optional stop model with a distance unit expressed as ATR or a percent of price
Notes. Backward compatibility Yes. Inputs migrated Yes.
Continuation Index [DCAUT]█ Continuation Index
📊 OVERVIEW
Continuation Index (CI) is an advanced trend analysis indicator developed by John F. Ehlers. This indicator provides early warning signals for trend onset, continuation, and exhaustion, with values oscillating between -1 and +1 to offer clear trend state identification for traders.
Based on the article TASC 2025.09 "Trend Onset And Trend Exhaustion - The Continuation Index" by John F. Ehlers.
💡 CORE VALUE
Unlike traditional trend indicators, the Continuation Index provides:
- Advanced dual-filter architecture (Ultimate Smoother + Laguerre Filter)
- Inverse Fisher Transform for enhanced signal-to-noise ratio
- Adaptive gamma parameter allowing market-specific tuning
- Binary state output (+1/-1) eliminating interpretation ambiguity
🎯 CONCEPTS
Signal Interpretation
CI > 0.5 : Strong bullish trend continuation - consider holding/adding long positions
CI = +1 : Maximum bullish signal - strong uptrend in progress
CI < -0.5 : Strong bearish trend continuation - consider holding/adding short positions
CI = -1 : Maximum bearish signal - strong downtrend in progress
CI near 0 : Neutral zone - trend uncertain, wait for clear signals
Brief pullbacks from extreme states : Potential reentry opportunities in trend direction
Primary Applications
Trend Onset Detection : Early warning signals for trend initiation
Trend Exhaustion Signals : Identify potential trend reversals
Position Management : Clear binary states for entry/exit decisions
Market Timing : Adaptive filtering reduces false signals
📋 PARAMETER SETUP
Source : Data source for calculation (default: close)
Length : The calculation length for the filters (default: 40, min: 1)
Gamma : Controls the phase response of the Laguerre filter. Smaller values increase responsiveness (default: 0.8, range: 0.0-1.0)
Laguerre Order : The order of the Laguerre filter, which directly affects its lag (default: 8, range: 1-10)
📊 COLOR CODING
Green : CI > 0.5 - Bullish trend continuation
Red : CI < -0.5 - Bearish trend continuation
Gray : Neutral zone - Trend unclear
