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Trending or mean-reverting? The Hurst exponent classifies regimes.
Hurst exponent is a measure of long-range autocorrelation in a time series, between 0 and 1. H = 0.5 indicates a random walk; H > 0.5 indicates persistence (trending behavior); H < 0.5 indicates mean reversion. Computed via rescaled-range (R/S) analysis or detrended fluctuation analysis (DFA).
log(R/S) ~ H · log(N)log(R/S) ~ H · log(N)For each window size N, compute the rescaled range. Regress log(R/S) on log(N). The slope is H.
Hurst exponent helps classify a market regime. A trend-following strategy works in H > 0.5 environments; a mean-reversion strategy works in H < 0.5. Equity indices typically run slightly above 0.5 (modest persistence), which is why momentum factors have historically been profitable.
For S&P 500 daily returns 1928–present, Hurst exponent computed via DFA is approximately 0.53 — slightly trending. For BTC, H ≈ 0.58. For mean-reverting commodity spreads, H ≈ 0.35.
H below 0.5 favors mean-reversion strategies. H above 0.5 favors trend-following. H near 0.5 means random-walk — no exploitable pattern.
Volatility · K-Ratio · Beta
Foliolytic uses Detrended Fluctuation Analysis (DFA), which is more robust than classical rescaled-range analysis to nonstationary data.
Persistence — past trends tend to continue. Trend-following strategies are favored.
Mean reversion — past trends tend to reverse. Mean-reversion strategies are favored.
Yes — in the advanced metrics section.
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