Exact and Approximate Maximum Likelihood Estimators for Vector Moving Average Processes

Summary This paper derives the exact likelihood function for the vector moving average process; the method used is a generalization of that adopted by Box and Jenkins (1970, Appendix A7.4) for the univariate process. Tunnicliffe Wilson (1973) has previously considered the estimation of parameters in multivariate time series models, and his procedure for moving averages is shown to be an approximation to maximum likelihood. A procedure for the computation of the exact likelihood function is also suggested.