The exact likelihood function of multivariate autoregressive-moving average models

By making use of the properties of tensor products, this paper describes the derivation of an expression for the exact likelihood function of a stationary process generated by a vector autoregressive-moving average model using concentrated maximum likelihood techniques. Furthermore, in the process of deriving the likelihood function, a closed form expression for the covariance function of the process in terms of the coefficients of the model is derived.