Testing Price Mean Reversion with ADF and Hurst Exponent

Summary

This article introduces statistical tools for assessing whether a price series is mean reverting, random-walking, or trending. It explains the Augmented Dickey-Fuller test as a unit-root test: the null hypothesis represents a random walk, and a sufficiently negative test statistic relative to critical values supports rejecting that null. The example applies the test to Google adjusted closing prices and reports that the null cannot be rejected for the sample examined.

It also describes the Hurst exponent as a way to characterize how price variation scales across time lags. The article associates values below 0.5 with mean reversion, values near 0.5 with random-walk behavior, and values above 0.5 with trending. Its examples include simulated series and Google, whose reported estimate is near 0.5. These diagnostics do not establish a tradable edge: the article notes that statistical significance of the Hurst estimate remains to be assessed and presents cointegration and strategy construction as later topics. Test results depend on modeling choices and the sample used.

Key ideas

• Mean reversion describes a tendency for a time series to move back toward a historical mean.
• The ADF test evaluates a unit-root null associated with random-walk behavior, with rejection requiring a statistic beyond the relevant critical value.
• The article’s ADF example does not reject the random-walk null for the sampled Google price series.
• The Hurst exponent characterizes scaling behavior, with values below, near, or above 0.5 associated respectively with mean reversion, random-walk behavior, or trending.
• A diagnostic estimate alone does not show that a series has statistically significant or tradable mean reversion.

Tags

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