Fractal Hurst Exponent & R/S Analysis (Model 05) | KoshX Learning
Classifying market regimes between trending persistence (H > 0.5) and mean-reverting anti-persistence (H < 0.5) using rescaled range analysis.
Empirical Quantitative Methodology
Rescaled range (R/S) analysis computes the empirical Hurst Exponent to identify whether price movement exhibits persistent long-memory trends (H > 0.5), random walk behavior (H = 0.5), or mean-reverting chop (H < 0.5). Only persistent regimes are eligible for trend-following models.
(R/S)_n = c \cdot n^H, \quad \log(R/S)_n = \log c + H \log n
Frequently Asked Questions
What does the Hurst Exponent (H) measure in equity markets?
Developed by hydrologist H.E. Hurst and applied to finance by Benoit Mandelbrot, the Hurst Exponent quantifies long-term memory in time series. H > 0.5 signifies persistent trending (past gains predict future gains). H = 0.5 denotes geometric Brownian motion (random walk). H < 0.5 denotes anti-persistent mean reversion (price reverses constantly).
Why should swing traders avoid stocks with H < 0.45?
Stocks with H < 0.45 are mathematically dominated by mean-reverting chop and noise. Breakout strategies on these stocks have a failure rate exceeding 70%, leading to whipsaws and wasted MTF margin interest charges.
How does KoshX combine the Hurst Exponent with Momentum?
KoshX only deploys trend-following and momentum models (Models 01, 02, and 03) when a stock’s Hurst Exponent is confirmed above 0.55. If H drops below 0.45, the terminal automatically switches to Model 04 (Ornstein-Uhlenbeck) for mean-reverting tactics.