248. Summary

249. ARIMA family (Box-Jenkins models)

■ AR ■ MA ■ differencing

Each model is written using the backshift operator , where and . The compact form

expresses ARIMA as a product of three operators acting on the series: the AR polynomial, the differencing operator, and the MA polynomial. is white noise with mean zero and variance .

For multivariate models, is a vector of time series, and operator coefficients become matrices.

249.1. Univariate models

249.2. Multivariate (vector) models

For all models below, is a vector of jointly modeled time series. Operator coefficients and are matrices, and is multivariate white noise with covariance matrix .