# mean-reversion

Statistical toolkit for mean-reversion trading strategies. Validates stationarity with ADF and Hurst tests, calculates half-life, and generates z-score trade signals.

- skill · `type=skill` · Claude Code, Codex, Cursor, GitHub Copilot, Gemini CLI, OpenCode · 490 installs · ★ 443
- Author: agiprolabs
- License: MIT · policy=mirror · the beginning of the file is at the end of this page
- Source: https://github.com/agiprolabs/claude-trading-skills/tree/HEAD/skills/mean-reversion/SKILL.md
- Updated: 2026-09-03
- HTML: https://affpapa.org/en/nevibecode/skills/mean-reversion

## What it does

This skill provides mathematical tools to test whether a price series or asset spread tends to return to its historical average. It verifies stationarity using the Augmented Dickey-Fuller test, the Hurst exponent, or variance ratio tests. A Hurst value below 0.5 confirms mean-reverting behavior. Random walks get filtered out immediately.

The implementation provides Python formulas relying on `numpy`, `scipy`, and `statsmodels`. It estimates mean-reversion half-life via AR(1) linear regression. That half-life governs trade management: the lookback window is set to twice the half-life, standard holding periods equal one half-life, and stop exits trigger at three. Continuous-time dynamics are handled through Ornstein-Uhlenbeck process parameters.

Mean reversion fails during persistent market trends or structural breaks such as token migrations. Wide spreads in illiquid pairs will also erase calculated profits.

## Install

### Claude Code (native platform)

1. **Skills CLI (Vercel)**
```bash
npx skills add agiprolabs/claude-trading-skills --skill mean-reversion -a claude-code
```

2. **Manually: put the files in place**
- File: `~/.claude/skills/mean-reversion/SKILL.md` — Copy the whole skill folder; for one project use .claude/skills/mean-reversion/

### Codex

1. **Skills CLI (Vercel)**
```bash
npx skills add agiprolabs/claude-trading-skills --skill mean-reversion -a codex
```

2. **Manually: put the files in place**
- File: `.agents/skills/mean-reversion/SKILL.md` — For all projects use ~/.agents/skills/

### Cursor

1. **Skills CLI (Vercel)**
```bash
npx skills add agiprolabs/claude-trading-skills --skill mean-reversion -a cursor
```

2. **Manually: put the files in place**
- File: `.cursor/skills/mean-reversion/SKILL.md` — Cursor also reads .agents/skills/ and .claude/skills/

### GitHub Copilot

1. **GitHub CLI**
```bash
gh skill install agiprolabs/claude-trading-skills mean-reversion
```

2. **Manually: put the files in place**
- File: `.github/skills/mean-reversion/SKILL.md`

### Gemini CLI

1. **Skills CLI (Vercel)**
```bash
npx skills add agiprolabs/claude-trading-skills --skill mean-reversion -a gemini-cli
```

2. **Platform CLI**
```bash
gemini skills install https://github.com/agiprolabs/claude-trading-skills --path skills/mean-reversion
```

### Windsurf (Devin Desktop)

**Manually: put the files in place**
- File: `.devin/skills/mean-reversion/SKILL.md` — The legacy .windsurf/skills/ path still works

### OpenCode

**Skills CLI (Vercel)**
```bash
npx skills add agiprolabs/claude-trading-skills --skill mean-reversion -a opencode
```

### Claude.ai

**Claude.ai**
- Zip the folder and upload it in Settings → Capabilities → Skills

Where a file is given instead of a command, copy the files from the source to that path: https://github.com/agiprolabs/claude-trading-skills/tree/HEAD/skills/mean-reversion/SKILL.md

## When to use it
- test price stationarity using the Augmented Dickey-Fuller test
- compute the Hurst exponent to identify mean-reverting series
- estimate mean-reversion half-life using an AR(1) regression model
- generate entry and stop signals with normalized z-scores
- estimate parameters for the Ornstein-Uhlenbeck continuous process

## Example prompts
- Run an ADF test and compute the Hurst exponent on this price series.
- Estimate the half-life for this spread and generate z-score entry signals.
- Fit Ornstein-Uhlenbeck parameters theta and mu to the token returns.

## Source text · SKILL.md · MIT

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BEGIN THIRD-PARTY FILE 891d8b01c44f9c02
````text
---
name: mean-reversion
description: Mean-reversion strategy tools including Hurst exponent, half-life estimation, z-score signals, ADF testing, and Ornstein-Uhlenbeck modeling
---

# Mean Reversion

Mean reversion is the statistical tendency for prices, spreads, or other financial variables to return toward a long-run average after deviating from it. A mean-reverting series overshoots its mean, then corrects back -- creating predictable oscillations that can be traded.

## When Mean Reversion Works

- **Ranging markets**: Sideways price action with clear support/resistance
- **Pairs spreads**: Spread between cointegrated assets reverts to equilibrium
- **Oversold/overbought extremes**: RSI, Bollinger Band, or z-score extremes in stationary series
- **Funding rate arbitrage**: Perpetual funding rates revert to baseline
- **Stablecoin depegs**: Classic mean-reversion opportunity (peg = known mean)
- **Post-dump recovery**: Brief mean-reversion windows after initial PumpFun dumps

## When Mean Reversion Fails

- Strong trending markets (most crypto most of the time)
- Regime changes: what was stationary becomes non-stationary
- Structural breaks: token migration, protocol upgrade, delistings
- Low liquidity: wide spreads consume mean-reversion profits

---

## Testing for Mean Reversion

Before trading mean reversion, you must statistically confirm the series is mean-reverting. Three complementary tests:

### 1. Augmented Dickey-Fuller (ADF) Test

Tests the null hypothesis that a series has a unit root (non-stationary).

```python
from scipy import stats
import numpy as np

def adf_test(series: np.ndarray, max_lag: int = 0) -> dict:
    """Run ADF test. Reject null (p < 0.05) → stationary → mean-reverting."""
    # See references/statistical_tests.md for full implementation
    # Use statsmodels.tsa.stattools.adfuller for production
    pass
```

- **p < 0.01**: Strong evidence of stationarity
- **p < 0.05**: Evidence of stationarity
- **p > 0.10**: Cannot reject unit root -- likely non-stationary

### 2. Hurst Exponent

Measures the long-range dependence of a time series.

| Hurst Value | Interpretation | Trading Implication |
|-------------|---------------|---------------------|
| H < 0.5     | Mean-reverting | Trade mean reversion |
| H = 0.5     | Random walk    | No edge             |
| H > 0.5     | Trending       | Trade momentum       |

```python
def hurst_exponent(series: np.ndarray) -> float:
    """Compute Hurst exponent via R/S method. H < 0.5 → mean-reverting."""
    # See references/statistical_tests.md for full R/S algorithm
    pass
```

### 3. Variance Ratio Test
````
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