Is the market trending or chopping? Regime detection with the Hurst Exponent, Shannon Entropy and FDI

Most losing trades do not happen because an indicator is broken. They happen because a trend-following rule is fired inside a mean-reverting sideways range — or a mean-reversion rule steps in front of a persistent trend.

Short answer: you can measure the regime mathematically before taking a trade. The Hurst Exponent (hurst(close, 36)), Shannon Entropy (entropy(close, 20)) and Sevcik Fractal Dimension Index (fdi(close, 30)) quantify whether price has positive memory (trend), negative memory (mean reversion), or maximum disorder (noise).

Three mathematical lenses on market structure

**Hurst Exponent (hurst(src, n)):** originally developed by hydrologist Harold Edwin Hurst to study Nile river floods via Rescaled Range ($R/S$) analysis.
$H = 0.50$: geometric Brownian walk (no memory).
$H > 0.55$: persistent series — up moves are statistically more likely to be followed by up moves. Breakout and momentum strategies belong here.
$H < 0.45$: anti-persistent series — rallies tend to revert. Z-Score and WaveTrend pullback rules belong here.
**Shannon Information Entropy (entropy(src, n)):** maps the probability distribution of bar-to-bar returns onto $[0, 1]$. When entropy climbs above $0.85$, return buckets are nearly uniform — pure disorder where reducing exposure saves fee bleed.
**Sevcik Fractal Dimension (fdi(src, n)):** measures how much of the 2D plane the price curve fills between $1.0$ (a straight line) and $2.0$ (space-filling noise). Clean trends sit below $1.45$; choppy ranges sit above $1.55$.

Regime-Conditional Information Coefficient in the Lab

In the Indicator Lab, every custom formula is now evaluated not only across the full sample, but split into four distinct regimes:

Trend IC vs. Range IC (classified by ADX and Choppiness structure)
High-Volatility IC vs. Low-Volatility IC

That split immediately reveals whether your indicator is a trend filter or a range oscillator, so you can gate it properly in Strategy Studio.

This is research, not investment advice.