Seasonal ARIMA models

Let’s look at another characteristic of time series called seasonality. Seasonality is the presence of a pattern in a time series that repeats at regular intervals. Seasonal time series are common in nature. For example, yearly weather patterns and daily sunshine patterns are seasonal patterns. Back at the start of the non-stationary section, we showed an example of a non-stationary time series with seasonality. This time series is shown again in Figure 11.22 along with its ACF plot.

Figure 11.22 – Airline volume data and ACF plot

The time series shown in Figure 11.22 is the monthly total of international airline passengers from 1949 to 1960 [3]. There is a definite repeated pattern in this time series. To model this type of data, we will need to an additional term to the ARIMA model to account for seasonality.

Seasonal differencing

We will use a similar approach for modeling this type of time series as we did...