Hands-On Machine Learning for Algorithmic Trading

Unit root tests

Statistical unit root tests are a common way to determine objectively whether (additional) differencing is necessary. These are statistical hypothesis tests of stationarity that are designed to determine whether differencing is required.

The augmented Dickey-Fuller (ADF) test evaluates the null hypothesis that a time series sample has unit root against the alternative of stationarity. It regresses the differenced time series on a time trend, the first lag, and all lagged differences, and computes a test statistic from the value of the coefficient on the lagged time series value. statsmodels makes it easy to implement (see companion notebook).

Formally, the ADF test for a time series, y_t, runs the linear regression:

Where ...