In statistics, an augmented Dickey–Fuller test (ADF) tests the null hypothesis that a unit root is present in a time series sample.
The alternative hypothesis depends 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.
(See that article for a discussion on dealing with uncertainty about including the intercept and deterministic time trend terms in the test equation.)
By including lags of the order p, the ADF formulation allows for higher-order autoregressive processes.
This means that the lag length p must be determined in order to use the test.
One approach to doing this is to test down from high orders and examine the t-values on coefficients.
The unit root test is then carried out under the null hypothesis
If the calculated test statistic is less (more negative) than the critical value, then the null hypothesis of
In contrast, when the process has no unit root, it is stationary and hence exhibits reversion to the mean - so the lagged level will provide relevant information in predicting the change of the series and the null hypothesis of a unit root will be rejected.
A model that includes a constant and a time trend is estimated using sample of 50 observations and yields the
This is more negative than the tabulated critical value of −3.50, so at the 95% level, the null hypothesis of a unit root will be rejected.