4.8.2 Moving-Average Processes

4.8.2  Moving-Average Processes

An n-dimensional moving-average process of order q, MA(q), has form


where a is an n-dimensional vector, the βk are n matrices, and W is n-dimensional white noise. The coefficients βk of [4.50] induce autocorrelations in an MA process. In applications, MA(1) and MA(2) processes are common.

Exhibit 4.11 indicates a realization of the univariate MA(2) process


where W is variance 1 Gaussian white noise.

Exhibit 4.11: A realization of MA(2) process [4.54].