ADF Test

Augmented Dickey-Fuller Test

• This is a statistical procedure to determine whether a time series is stationary or not.
• We will discuss more details about the test in the next lectures.
• For now, that’s what we need to know:
  1. Null hypothesis: $H_0$: the series is nonstationary.
  2. Alternative hypothesis: $H_A$: the series is stationary.

Dickey-Fuller test for sationarity

This is the main idea behind the Dickey-Fuller test for stationarity of time series (testing the presence of a unit root). If we can get a stationary series from a non-stationary series using the first difference, we call those series integrated of order 1. The null hypothesis of the test is that the time series is non-stationary, which was rejected on the first three plots and finally accepted on the last one. We have to say that the first difference is not always enough to get a stationary series as the process might be integrated of order d, d > 1 (and have multiple unit roots). In such cases, the augmented Dickey-Fuller test is used, which checks multiple lags at once.

unit root?