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 one-step estimator generally has smaller mean square error than 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 one-step estimator for processes with some unit roots is derived.

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