mean-reversion

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

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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).

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