PARTIAL · filter only
Hypothesis
The Hurst exponent $H$ distinguishes trending ($H>0.5$) from mean-reverting ($H<0.5$) regimes. Gating an existing momentum book to fire only when $H>0.55$ should cut whipsaw losses.
Math — rescaled-range Hurst
Estimate $H$ from the scaling of the rescaled range $R/S$ with window length $n$:
$$ \mathbb{E}\!\left[\frac{R(n)}{S(n)}\right] \sim c\, n^{H} $$
Fit $\log(R/S)$ vs $\log n$; the slope is $H$. $H=0.5$ is a random walk.
Method
Compute $H$ on rolling 256-bar log-returns (DFA cross-check). Use as a binary gate on a baseline EMA-cross momentum book across 50 symbols.
Results
| Baseline momentum Sharpe | 0.4 |
| Gated (H>0.55) Sharpe | 0.7 |
| Whipsaw trades removed | −31% |
| Signal lag from 256-bar window | ~4h |
Real as a filter, not a strategy. Gating momentum on $H>0.55$ lifts Sharpe 0.4→0.7 and cuts a third of whipsaws — but the 256-bar estimate lags, so it confirms regimes late. Useful overlay, no standalone edge.
Regime detectors are lagging by construction — they need enough data to estimate the regime, by which time it is partly over. Use them to veto, not to time.