A Likelihood Based Estimator for Vector Autoregressive Processes

A one-step estimator which is an approximation to the unconditional maximum likelihood estimator of the coefficient matrices of a Gaussian first order vector autoregressive process is presented. The one-step estimator is easy to compute and numerically stable. In finite samples the onestep estimator generally has smaller mean square error than the ordinary least squares estimator. When the process has one unit root, the onestep estimator of the parameter associated with the unit root has a mean square error that is about eighty percent of that of the ordinary least squares estimator. The estimation procedure is extended to higher order processes via the first order representation of higher order autoregressive processes. The limiting distribution of the onestep estimator for processes with some unit roots is derived.