Generalized Hurst Exponent and Variance Ratio Tests for Forex Mean Reversion

Summary

This article describes using the Generalized Hurst Exponent (GHE) to study time-series scaling and classify series as persistent, random-like, or mean reverting. Unlike the standard Hurst formulation, GHE varies the moment order q to examine different distributional features; the article highlights q values of 1 and 2. It also presents the Variance Ratio Test (VRT) as a statistical check on inferences drawn from GHE analysis and discusses implementing both methods in MQL5.

The application is screening forex symbols for mean-reversion behavior, then using a z-score indicator and a basic expert advisor to demonstrate entries and exits. The article discusses backtesting and points out that thresholds optimized on historical data may stop fitting as market conditions change. Its evidence is illustrative rather than conclusive: the provided material does not establish durable profitability, and fixed thresholds, selected lookback lags, and in-sample optimization can limit generalization. It suggests applying related tools to spreads between paired instruments as a possible extension.

Key ideas

• GHE evaluates how time-series scaling changes across different moment orders.
• The selected lag range affects the GHE estimate and should be treated as a modeling choice.
• The Variance Ratio Test can serve as a statistical check alongside GHE analysis.
• The article uses these methods to screen forex series for mean-reversion candidates.
• Fixed entry and exit thresholds may become unreliable as market dynamics change.

Tags

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.