1. Forecasting seasonal ARIMA
As in the nonseasonal case,
2. Forecasting ARIMA Processes
once a model is chosen, forecasting is easy because the model describes how the dynamics of the time series behaves over time.
You simply continue the model dynamics into the future.
In astsa, use sarima-dot-for for forecasting. It is similar to the sarima command, but you also specify the forecasting horizon.
3. Forecasting Air Passengers
Recall that we found that an SARIMA(0,1,1, 0,1,1,12) was the best model for the logged AirPassengers time series.
Now let's forecast 2 years beyond the end of the data. This can be done using sarima-dot-for as shown here. The data are show in black, the forecasts are red, and the gray swatches represent 1 and 2 root mean square prediction intervals.
4. Let's practice!