Testing Mean Reversion with ADF Stationarity Tests and the Hurst Exponent

Summary

This overview explains mean reversion as a tendency for a time series to move back toward a typical level, contrasting it with a random walk and relating the idea to the Ornstein–Uhlenbeck process. It describes the Augmented Dickey-Fuller test as a unit-root test: its null hypothesis is nonstationarity, and a sufficiently negative statistic relative to the relevant critical value supports rejecting that null. Lag selection and model specification affect the test, and the article notes that ADF does not test every property, such as changing variance or cointegration.

It also introduces the Hurst exponent as a measure of long-term dependence inferred from how variability scales with time horizon. Values below, above, or equal to 0.5 are presented as indicating anti-persistence, persistence, or random-walk-like behavior, respectively. These diagnostics can inform whether mean-reversion or trend-oriented analysis is plausible, but they do not establish a profitable strategy. The article’s Hurst calculation description is simplified, and stationarity tests require careful specification and interpretation; the text offers no trading results or empirical example.

Key ideas

• The Ornstein–Uhlenbeck process is presented as a model of continuous mean-reverting behavior.
• The ADF test evaluates a unit-root null, with rejection supporting stationarity under the selected model.
• ADF results depend on lag and trend choices and do not address every time-series property.
• The Hurst exponent characterizes persistence, anti-persistence, or random-walk-like scaling.
• Stationarity and dependence diagnostics can guide research but do not by themselves prove trading profitability.

Tags

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