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We consider a non stationary vector autoregressive process which is integrated of order 1, and generated by i.i.d Gaussian errors. We then derive the maximum likelihood estimator of the space of cointegration vectors and the likelihood ratio test of the hypothesis that it has a given number of dimensions. Further we test linear hypotheses about the cointegration vectors. The asymptotic distribution of these test statistics are found and one is described by a natural multivariate version of the usual test for a unit root in an autoregressive process, and the other by a χ² test.