Asymptotic properties of least squares statistics in general vector autoregressive models

A vector autoregression with deterministic terms with no restrictions to its characteristic roots is considered. Strong consistency results and also some weak convergence results are given for a number of least squares statistics. These statistics are related to the denominator matrix of the least squares estimator as well as the least squares estimator itself. Applications of these results to the statistical analysis of non-stationary economic time-series are briefly discussed.