For time series with seasonal effects, we can include AR and MA terms that capture the seasonality's periodicity. For instance, when using monthly data and the seasonal effect length is one year, the seasonal AR and MA terms would reflect this particular lag length.

The ARIMAX(p, d, q) model then becomes a SARIMAX(p, d, q) x (P, D, Q)_s model, which is a bit more complicated to write out, but the references on GitHub, including the statsmodels documentation, provide this information in detail.

We will now build a seasonal ARMA model using macro-data to illustrate the implementation.