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.
Contents
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.
Testing procedure
The testing procedure for the ADF test is the same as for the Dickey–Fuller test but it is applied to the model
where
By including lags of the order p the ADF formulation allows for higher-order autoregressive processes. This means that the lag length p has to be determined when applying the test. One possible approach is to test down from high orders and examine the t-values on coefficients. An alternative approach is to examine information criteria such as the Akaike information criterion, Bayesian information criterion or the Hannan–Quinn information criterion.
The unit root test is then carried out under the null hypothesis
is computed it can be compared to the relevant critical value for the Dickey–Fuller Test. If the test statistic is less (this test is non symmetrical so we do not consider an absolute value) than the (larger negative) critical value, then the null hypothesis of
Intuition
The intuition behind the test is that if the series is integrated then the lagged level of the series (
Examples
A model that includes a constant and a time trend is estimated using sample of 50 observations and yields the
Alternatives
There are alternative unit root tests such as the Phillips–Perron test (PP) or the ADF-GLS test procedure (ERS) developed by Elliott, Rothenberg and Stock (1996).