Augmented Dickey–Fuller test

In statistics and econometrics, an augmented Dickey–Fuller test (ADF) tests the null hypothesis of a unit root is present in a time series sample. The alternative hypothesis is different depending on which version of the test is used, but is usually stationarity or trend-stationarity. It is an augmented version of the Dickey–Fuller test for a larger and more complicated set of time series models.

The augmented Dickey–Fuller (ADF) statistic, used in the test, is a negative number. The more negative it is, the stronger the rejection of the hypothesis that there is a unit root at some level of confidence.

The testing procedure for the ADF test is the same as for the Dickey–Fuller test but it is applied to the model

where ${\displaystyle \alpha }$ is a constant, ${\displaystyle \beta }$ the coefficient on a time trend and ${\displaystyle p}$ the lag order of the autoregressive process. Imposing the constraints ${\displaystyle \alpha =0}$ and ${\displaystyle \beta =0}$ corresponds to modelling a random walk and using the constraint ${\displaystyle \beta =0}$ corresponds to modeling a random walk with a drift. Consequently, there are three main versions of the test, analogous to the ones discussed on Dickey–Fuller test (see that page for a discussion on dealing with uncertainty about including the intercept and deterministic time trend terms in the test equation.)

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