Exact Maximum Likelihood Estimation of Stationary Vector ARMA Models

Resumo

The problems of evaluating and maximizing the exact likelihood function of vector ARMA models are considered separately. A new and efficient procedure for evaluating the exact likelihood function is presented. This method puts together a set of useful features which can only be found separately in currently available algorithms. A procedure for maximizing the exact likelihood function, which takes full advantage of the properties offered by the evaluation algorithm, is also considered. Combining these two procedures, a new algorithm for exact maximum likelihood estimation of vector ARMA models is obtained. Comparisons with existing procedures, in terms of both analytical arguments and a numerical example, are given in order to show that the new estimation algorithm performs at least as well as existing ones, and that relevant real situations occur in which it do es better.