Maximum likelihood estimation for a multivariate autoregressive model

The paper provides an analytical expression for the exact log likelihood function and its first derivatives for a multivariate autoregressive model. Based on these results, two algorithms for constructing the maximum likelihood estimate, using the Fisher´s scoring technique, are proposed. The estimated model is guaranteed to be stable. Simulation examples show that this algorithm has good convergence properties and the resulting maximum likelihood estimator could perform better than earlier methods, in cases where the record length is short and the autoregressive polynomial has roots near the unit circle