Seasonal ARIMA

ARIMA($p$,$d$,$q$) models rely on the assumption that the underlying data is stationary or can be made stationary by differencing it $d$ number of times. However, some time series will not be stationary even after differencing. Seasonal series are a common example. Seasonality is a widespread phenomenon in time series analysis:

• People consume more during Christmas.

• Households consume less energy at night.

• Temperatures are higher in summer than in winter.

Fortunately for us, we can extend the logic of the ARIMA model to account for these seasonal (regular) variations. This is what the Seasonal Autoregressive Integrated Moving Average (SARIMA) model does.