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). 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 3. Variance Ratio Test Compares variance of multi period returns to single period variance. VR < 1 : Negative autocorrelation (mean reverting) VR = 1 : Random walk VR 1 : Positive autocorrelation (trending) See references/statistical tests.md for complete implementations and interpretation guides. Half Life Estimation The half life tells you how many periods it takes for a deviation to decay to half its size. This is the single most important parameter for mean reversion trading. AR(1) Regression Method Fit the autoregressive model: delta X t = alpha + beta X {t 1} + epsilon Using Half Life Parameter Rule of Thumb Lookback window 2x half life Holding period 1x half life Maximum hold 3x half life (stop) Signal recalc 0.5x half life Z Score Signal Framework The z score normalizes the deviation from the mean, providing standardized entry/exit signals. Signal Rules Condition Signal Action z < 2.0 Buy Enter long (price below mean) z +2.0 Sell Enter short (price above mean) z crosses 0 Exit Close position (returned to mean) abs(z) 3.0 Stop Close position (reversion failed) Lookback Window Set the rolling window to approximately 2x the half life : Position Sizing with Z Score Scale position size with z score magnitude for better risk adjusted returns: See references/strategy design.md for complete entry/exit framework and sizing. Ornstein Uhlenbeck (OU) Process The OU process is the continuous time model of mean reversion: Parameter Meaning Estimation theta Speed of mean reversion From AR(1) beta: theta = ln(1+beta)/dt mu Long run mean From AR(1) intercept: mu = alpha/beta sigma Volatility of innovations Residual std from AR(1) Parameter Estimation Strategy Types Single Asset Mean Reversion Apply z score framework directly to a token's price series. Works best on: Stablecoins (USDC/USDT spread) Tokens in established ranges After confirming stationarity with ADF test Pairs Trading Trade the spread between two cointegrated assets: 1. Confirm cointegration (see cointegration analysis skill) 2. Compute spread: S = Y beta X 3. Apply z score framework to the spread 4. Go long spread (buy Y, sell X) when z < 2 5. Go short spread (sell Y, buy X) when z +2 Statistical Arbitrage Multi asset extension of pairs trading: Eigenportfolios from PCA of correlated assets Trade the smallest eigenvalue portfolios (most mean reverting) Requires larger universe (10+ assets) Crypto Specific Considerations 1. Most crypto trends : Hurst exponent for BTC, ETH, SOL is typically 0.55 0.70. Raw price mean reversion is rare. 2. Where to find mean reversion : Pairs spreads (SOL/ETH ratio, BTC dominance) Funding rates on perpetuals Basis between spot and futures Stablecoin depegs Fee tier spreads across DEXs 3. Short lookbacks : Crypto mean reversion has short half lives (hours to days, not weeks) 4. Transaction costs : DEX swap fees (0.25 1%) can eat mean reversion profits. Factor in slippage. 5. Regime awareness : Use regime detection skill to only trade mean reversion in ranging regimes. Integration with Other Skills Skill Integration cointegration analysis Find cointegrated pairs for pairs trading pandas ta RSI, Bollinger Bands as mean reversion indicators regime detection Filter: only trade MR in ranging regimes vectorbt Backtest mean reversion strategies volatility modeling Estimate sigma for OU model slippage modeling Factor execution costs into P&L estimates position sizing Size positions using Kelly + z score scaling Files References references/statistical tests.md ADF, Hurst exponent, variance ratio, and half life estimation with full implementations and interpretation references/strategy design.md Z score framework, position sizing, pairs trading setup, risk management, and backtest considerations Scripts scripts/mean reversion test.py Comprehensive mean reversion analysis: ADF, Hurst, variance ratio, half life, OU estimation, z score signals scripts/pairs scanner.py Scan multiple assets for mean reverting pairs: correlation, cointegration, spread analysis, ranking Quick Start This skill provides analytical tools and information only. It does not constitute financial advice or trading recommendations.

mean-reversion