Tests to Determine Stationarity

Augmented Dickey-Fuller (ADF) Test:

• Null Hypothesis ([Tex]H_0[/Tex]): The time series has a unit root, indicating it is non-stationary.
• Alternate Hypothesis ([Tex]H_1[/Tex]): The time series does not have a unit root, indicating it is stationary.
• Test Statistic: The ADF test statistic is compared to critical values from the ADF distribution to determine whether the null hypothesis can be rejected.
• Decision Rule: If the test statistic is less than the critical value, the null hypothesis is rejected, and the series is considered stationary. Otherwise, if the test statistic is greater than the critical value, the null hypothesis is not rejected, and the series is considered non-stationary.

Kwiatkowski-Phillips-Schmidt-Shin (KPSS) Test:

• Null Hypothesis ([Tex]H_0[/Tex]): The series is stationary around a deterministic trend.
• Alternate Hypothesis ([Tex]H_1 [/Tex]): The series has a unit root, indicating it is non-stationary.
• Test Statistic: The KPSS test statistic is compared to critical values to determine whether the null hypothesis can be rejected.
• Decision Rule: If the test statistic is greater than the critical value, the null hypothesis is rejected, and the series is considered non-stationary. If the test statistic is less than the critical value, the null hypothesis is not rejected, and the series is considered stationary.

Removing non-stationarity in time series data is crucial for accurate forecasting because many time series forecasting models assume stationarity, where the statistical properties of the time series do not change over time. Non-stationarity can manifest as trends, seasonality, or other forms of irregular patterns in the data.

The article comprehensively covers techniques and tests for removing non-stationarity in time series data, crucial for accurate forecasting, including detrending, seasonal adjustment, logarithmic transformation, differencing, and ADF/KPSS tests for stationarity validation.