Maximum Likelihood Estimation and Model Checking for Vector ARMA Models

Abstract

In this chapter, conditional and exact maximum likelihood (ML) estimation procedures for vector ARMA time series models are presented and their properties are examined. For conditional maximum likelihood, explicit iterative computation of the ML estimator in the form of generalized least squares estimation is presented, while for the exact likelihood method, two different approaches to computation of the exact likelihood function are developed. ML estimation of vector ARMA models under linear constraints on the parameters, and associated LR testing of the hypothesis of the linear constraints are examined. Model checking techniques for an estimated model, based on correlation matrix properties of model residuals, are also explored. The effect of parameter estimation errors on mean square error for prediction from an estimated model is also considered. Two numerical examples of fitting and checking vector ARMA models are also presented.