Using CADF to Test Cointegration in Pairs Trading
Summary
The article explains how the Cointegrated Augmented Dickey-Fuller approach can assess whether a linear combination of two price series is stationary, a property that may support a mean-reversion pairs strategy. It contrasts this with applying an ordinary Augmented Dickey-Fuller test or the Hurst exponent to a spread formed using a hedge ratio chosen separately. The procedure fits an ordinary least squares regression to estimate the ratio, calculates residuals, and applies an ADF test to those residuals.
An example uses adjusted prices for Exxon Mobil and the United States Oil Fund over 2019. Its reported test statistic is more negative than the stated 5% critical value, so the article rejects the no-cointegration null for that sample. This is evidence about the selected historical period, not proof of a durable relationship or profitable strategy. The article recommends combining time-series tests with strategy-level performance analysis, since statistical stationarity does not establish trading returns.
Key ideas
- CADF combines hedge-ratio estimation by regression with a stationarity test on the resulting residuals.
- A stationary spread can provide a basis for mean-reversion trading even when individual assets are not mean reverting.
- The example reports evidence of cointegration between XOM and USO for the historical period analyzed.
- A finding for one sample does not establish that the relationship will persist or produce profits.
- Time-series statistical tests complement, rather than replace, trade-level performance analysis.
Tags
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.