Autoregressive Integrated Moving Average (ARIMA)

The “Autoregressive Integrated Moving Average” model is a non-seasonal time series method that combines three techniques when producing predictions. The first, corresponding to the “AR”, indicates the autoregressive component. This component regresses the desired variable over its previous values. The order of this portion of the model is specified by the parameter p. The second, corresponding to the “MA”, indicates the moving average component and is a regression of the desired variable’s errors over its previous values. The order of this portion of the model is specified by the parameter q. The third, corresponding to the “I”, indicates the integrated or differencing component and is a differencing of each value and its previous value. The order of this portion (number of times to perform differencing) is denoted by the parameter d. The differencing “I” component is performed before the “AR” and “MA” components are fit. The overall ARIMA is the combination of each of these three components into one condensed model.

NOTE: The ARIMA model is only capable of handling data with a trend component but no seasonal component.

Seasonal Autoregressive Integrated Moving Average (SARIMA)

The SARIMA model is a seasonal time series method and is an extension of the ARIMA modelling method. It contains the same three components of the ARIMA, however, a SARIMA adds an additional seasonal autoregressive, seasonal differencing, and seasonal moving-average component to the overall model in order to account for the recurring cycle of the data. The parameters for each of these additional seasonal components are denoted by P, D, and Qrespectively. The SARIMA also takes in a seasonal parameter s which accounts for the length of a singular cycle in the data.