Hi everyone,
Can someone please explain the difference between Covariance Stationary and Serial Correlation. My understanding was that a model that is covariance stationary should have no serial correlation. However, I found this paragraph in the text:
“Step D: If you find serial correlation, prepare to use an auto regressive (AR) model by making it covariance stationary. This includes: • Correcting for a linear trend— use first differencing. • Correcting for an exponential trend—take natural log and first difference. • Correcting for a structural shift— estimate the models before and after the change. • Correcting for seasonality— add a seasonal lag (see Step G). Step E: After the series is covariance stationary, use an AR(1) model to model the data. • Test residuals for significant serial correlations. • If no significant correlation, model is okay to use.”
If we already made the model covariance stationary in D (I assume this means it would already be free of serial correlation through testing via Dickey Fuller test etc. Furthermore, first differencing should have made it covariance stationary?), why do we still need to test it for serial correlation in E?
Thank you.