Separable Covariance Matrices and Kronecker Approximation

When a model structure allows for the error covariance matrix to be written in the form of the Kronecker product of two positive definite covariance matrices, the estimation of the relevant parameters is intuitive and easy to carry out. In many time series models, the covariance matrix does not have a separable structure. Van Loan and Pitsanis (1993) provide an approximation with Kronecker products. In this paper, we apply their method to estimate the parameters of a multivariate regression model with autoregressive errors. An illustrative example is also provided.