Why is testing for stationarity important in time series modeling, and which test is commonly used for this purpose?

Stationarity is critical in time series modeling because most statistical forecasting methods assume that the series has a constant mean and variance over time. Stationary data are easier to model and predict because they lack trends and cyclical patterns that could distort analysis. The Dickey-Fuller Test, particularly its augmented version (ADF Test), is commonly used to check for stationarity by testing the null hypothesis that the series has a unit root (indicating non-stationarity). If the test rejects the null hypothesis, it indicates that the series is stationary, allowing for more reliable and robust modeling. Option A (Granger Causality Test) is incorrect as it tests causality, not stationarity. Option C (Augmented Linear Test) is incorrect because no such test exists for seasonality. Option D (Residual Variance Test) is incorrect; stationarity is not concerned with residual variance but overall series stability. Option E (Z-Test) is incorrect because it assesses differences in means, not stationarity.