Using the Augmented Dickey-Fuller Test to Screen Pairs for Mean Reversion

Summary

The document explains how the Augmented Dickey-Fuller test can help assess whether the residuals between two securities are stationary, a condition used in pairs trading. It introduces stationarity, non-stationarity, unit roots, and the test’s null and alternative hypotheses. It also distinguishes the augmented test from the basic Dickey-Fuller test and outlines the idea of adding lagged difference terms to account for more complex time series behavior.

The practical walkthroughs describe regressing one stock’s price on another, testing the regression residuals, and comparing the test statistic or p-value with a chosen threshold. An Excel example uses two pharmaceutical stocks and reports a result that the text interprets as cointegration; a Python example with Apple and Microsoft concludes that the pair does not pass its stated checks. The examples illustrate screening, not proof that a pair will remain stable or produce profitable trades. The article also notes that historical relationships may not persist and that statistical analysis is required.

Key ideas

• The ADF test evaluates a time series for a unit root, with a unit root corresponding to non-stationarity.
• Pairs trading commonly tests whether the residuals from a relationship between two securities are stationary.
• The null hypothesis is a unit root, while the alternative indicates stationarity under the test specification.
• A practical workflow estimates a hedge relationship, forms residuals, and applies the ADF test to those residuals.
• A passing statistical test does not guarantee that a pair relationship will persist or make trading profitable.

Tags

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