In the previous chapter, we covered the autoregressive integrated moving average model, ARIMA(p,d,q), which allows us to model non-stationary time series. Now we’ll add another layer of complexity to the ARIMA model to include seasonal patterns in time series, leading us to the SARIMA model.
The seasonal autoregressive integrated moving average (SARIMA) model, or SARIMA(p,d,q)(P,D,Q)m, adds another set of parameters that allows us to take into account periodic patterns when forecasting a time series, which is not always possible with an ARIMA(p,d,q) model.
In this chapter, we’ll examine the SARIMA(p,d,q)(P,D,Q)m model and adapt our general modeling procedure to account for the new parameters. We’ll also determine how to identify seasonal patterns in a time series and apply the SARIMA model to forecast a seasonal time series. Specifically, we’ll apply the model to forecast the total number of monthly passengers for an airline. The data was recorded from January 1949 to December 1960. The series is shown in figure 8.1.
