ADF, Johansen, and Engle–Granger Tests for Cointegration Trading

Summary

This guide explains how unit-root and cointegration tests can help identify mean-reverting combinations of asset prices. It presents the Augmented Dickey–Fuller test as a test of whether price changes depend on the current level, and relates the estimated adjustment rate to a mean-reversion half-life. That estimate can inform choices such as lookback windows, though the text cautions that a near-zero or positive adjustment rate implies slow or absent mean reversion. It also describes forming a long-short spread from cointegrated assets, while warning that a statistically stationary combination may have coefficients unsuitable for a practical spread.

The Johansen method extends testing to multiple series and supplies cointegrating vectors that can serve as hedge ratios. The Engle–Granger procedure first checks that series share an integration order, then tests regression residuals for a unit root. The material is methodological, not a performance study: it provides no empirical trading results, and inference depends on test assumptions and appropriate data preparation.

Key ideas

• The ADF test evaluates whether a price series tends to adjust based on its previous level.
• The estimated adjustment rate can be used to approximate a mean-reversion half-life and guide strategy lookbacks.
• Cointegration can support long-short portfolios, but a stationary vector may not yield practical spread weights.
• Johansen testing handles multiple price series and provides vectors that can be used as hedge ratios.
• Engle–Granger testing requires compatible integration orders before testing regression residuals for stationarity.

Tags

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