8 Accounting for seasonality
This chapter covers
- Examining the seasonal autoregressive integrated moving average model or SARIMA(p,d,q)(P,D,Q)m
- Analyzing seasonal patterns in a time series
- Forecasting using the SARIMA(p,d,q)(P,D,Q)m model
In the previous chapter, we covered the autoregressive integrated moving average model or ARIMA(p,d,q), which allows to model non-stationary time series. Now, we 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 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 examine the SARIMA(p,d,q)(P,D,Q)m model and adapt the general modeling procedure to account for the new parameters. We also determine how to identify seasonal patterns in a time series, and finally apply the SARIMA model to forecast a seasonal time series.
Specifically, we 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.
Figure 8.1 Monthly total number of air passengers for an airline, from January 1949 to December 1960. We notice a clear seasonal pattern in the series, with peak traffic occurring towards the middle of each year.
