ADF (Augmented Dickey-Fuller) Test:
The Augmented Dickey-Fuller (ADF) test is a statistical test used to determine whether a given time series is stationary or non-stationary. It is based on the null hypothesis that the series has a unit root, meaning it is non-stationary. The ADF test computes a test statistic and compares it to critical values from a specific distribution to assess whether the null hypothesis can be rejected.
If the calculated test statistic is less than the critical value, the null hypothesis is rejected, indicating that the series is stationary. Conversely, if the test statistic is greater than the critical value, the null hypothesis cannot be rejected, suggesting that the series is non-stationary.
The ADF test can be performed with different specifications, including with or without a trend and with or without a constant term. The choice of specification depends on the characteristics of the time series being analyzed.
KPSS (Kwiatkowski-Phillips-Schmidt-Shin) Test:
The Kwiatkowski-Phillips-Schmidt-Shin (KPSS) test is another statistical test used to assess the stationarity of a time series. Unlike the ADF test, which tests for the presence of a unit root (non-stationarity), the KPSS test examines whether a series is trend-stationary or difference-stationary.
A trend-stationary series is one where the mean and variance are constant over time, but the series may exhibit a deterministic trend. In contrast, a difference-stationary series is one where the mean and variance change over time due to the presence of a stochastic trend.
Similar to the ADF test, the KPSS test computes a test statistic and compares it to critical values from a specific distribution to determine whether the null hypothesis can be rejected. The null hypothesis of the KPSS test is that the series is stationary, while the alternative hypothesis is that it is non-stationary.