A note on obtaining the theoretical autocovariances of an ARMA process

Abstract

We point out that to obtain the theoretical autocovariances of any vector ARMA process we need to solve a smaller system of equations than in Ansley (1980). This implies a substantial reduction in computation time. As an application, we consider obtaining the likelihood of a stationary ARMA process. To speed up the computation, we suggest a stable fixed point iteration.

Keywords:

• Covariances
• vector ARMA
• computation
• iteration