The ADF test is an extension of the Dickey-Fuller test and addresses the issue of higher-order autocorrelation by including lagged differences of the time series in the model. The test involves estimating the following regression:
Δyt is the first difference of the series. α is a constant. β is the coefficient on a time trend. γ is the coefficient of the lagged level of the series. δi are the coefficients of the lagged differences. εt is the error term.
The null hypothesis (H0) of the ADF test is that the time series has a unit root (i.e., it is non-stationary), while the alternative hypothesis (H1) is that the time series is stationary.
