Computation of the exact likelihood function of multivariate moving average models

This paper proposes three methods for computing the exact likelihood function of multivariate moving average models. Each method utilizes the structure of the covariance matrix in a different way. Formulae for operation counts of the three algorithms are given as a guide in selecting the best method for a given problem. Monte Carlo simulations are performed to compare the mean squared errors of parameter estimates obtained by maximizing the exact likelihood function versus those obtained by maximizing various approximate forms of the likelihood function.