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.