Exponential-Decay Cumulative Spread (Cycle-Tuned)

## Indicator Overview

**Exponential-Decay Cumulative Spread (Cycle-Tuned)** – short title **LambdaCumDelta** – tracks the percentage spread between CEXs BTC spot prices.
By clipping outliers, applying an exponential-decay running sum, and comparing that sum to rolling percentile bands, the script flags potential **cycle bottoms** and **cycle tops** whenever the cumulative spread stays beyond extreme thresholds for three consecutive bars.

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### Core Logic

1. **Price Spread**
`spread_pct = (cexA – cexB) / cexB × 100`.

2. **Outlier Suppression**

* Calculates the **90-day standard deviation σ** of `spread_pct`.
* Uses a **clip coefficient `k_clip`** (0.5–5.0) to cap the spread at `±k_clip × σ`, damping single-day anomalies.

3. **Exponential-Decay Sum**

* Applies a decay factor **λ** (0.50–0.999):

```
CumΔₜ = spread_clipₜ + λ × CumΔₜ₋₁
```
* Larger λ → longer memory half-life.

4. **Rolling Percentile Bands**

* Uses a **365-bar window** to derive dynamic percentile thresholds.
* Upper / Lower bands are set by **perc\_hi** and **perc\_lo** (e.g., 85 % and 15 %).

5. **Signal Definition**

* **Bullish** (cycle bottom): `CumΔ` above the upper band for **3 straight bars**.
* **Bearish** (cycle top): `CumΔ` below the lower band for **3 straight bars**.

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### Chart Elements

| Plot | Style | Meaning |
| --------------- | ----------------- | ----------------------------------- |
| **CumΔ** | Teal thick line | Exponential-decay cumulative spread |
| Upper Threshold | Green thin line | Rolling upper percentile |
| Lower Threshold | Red thin line | Rolling lower percentile |
| Background | Faded green / red | Bullish / bearish signal zone |

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### Key Inputs

| Input | Default | Purpose |
| -------------------- | ------- | ------------------------------- |
| **Decay factor λ** | 0.95 | Memory length of CumΔ |
| **Clip coefficient** | 2.0 | Multiple of σ for outlier cap |
| **Upper percentile** | 85 | Cycle-bottom trigger percentile |
| **Lower percentile** | 15 | Cycle-top trigger percentile |

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### Practical Tips

1. **Timing bias**

* Green background often precedes mean-reversion of the spread – consider scaling into longs or covering shorts.
* Red background suggests stretched positive spread – consider trimming longs or lightening exposure.
2. **Combine with volume, trend filters (MA, MACD, etc.)** to weed out false extremes.
3. Designed for **daily charts**; ensure both exchange feeds are synchronized.

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### Alerts

Two built-in `alertcondition`s fire when bullish or bearish criteria are met, enabling push / email / webhook notifications.

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### Disclaimer

This script is for educational and research purposes only and is **not** financial advice. Test thoroughly and trade at your own risk.