An n-dimensional autoregressive process of order p, AR(p), has form
where a is an n-dimensional vector, the bk are n×n matrices, and W is n-dimensional white noise. The name “autoregressive” indicates that [4.52] defines a regression of tX on its own past values. In applications, AR(1) and AR(2) processes are common.
Exhibit 4.12 indicates a realization of the univariate AR(2) process
where W is variance 1 Gaussian white noise.
Exhibit 4.12: A realization of AR(2) process [4.56].