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

[4.57]

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

[4.58]

where W is variance 1 Gaussian white noise.

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