Seasonal ARIMA Model

Definition

A Multiplicative Seasonal ARIMA Model, denoted as $\text{ARIMA}(p,d,q)\times (P,D,Q{)}_s$, applies both non-seasonal differencing (order $d$) and seasonal differencing (order $D$) to achieve stationarity.

If the differenced series:

$$W_t={\nabla }^d{\nabla }_s^D{Y}_t$$

satisfies an $\text{ARMA}(p,q)\times (P,Q{)}_s$ model, then the original series $Y_t$ is called a Seasonal ARIMA model.

Interpretation

This is a comprehensive model handling non-stationarity in mean (both trend and seasonality) and modeling the remaining stationary component with AR and MA terms at both seasonal and non-seasonal lags.

Specification, Fitting, and Checking

The procedures for specification, fitting, and diagnostic checking for seasonal models follow the same general techniques as non-seasonal models.