4.8.4 Autoregressive Moving-Average Processes

4.8.4  Autoregressive Moving-Average Processes

An n-dimensional autoregressive moving-average process of orders p and q, ARMA(p,q), has form


As the name suggests, it combines an AR(p) model with an MA(q) model of the same dimension n. In applications, ARMA(1,1) processes are common.

Exhibit 4.13 indicates a realization of the univariate ARMA(1,1) process


where W is variance 1 Gaussian white noise.

Exhibit 4.13: A realization of ARMA process [4.58].