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This paper gives a systematic application of maximum likelihood inference concerning cointegration vectors in non-stationary vector valued autoregressive time series models with Gaussian errors, where the model includes a constant term and seasonal dummies. The hypothesis of cointegration is given a simple parametric form in terms of cointegration vectors and their weights. The relation between the constant term and a linear trend in the non-stationary part of the process is discussed and related to the weights. Tests for the presence of cointegration vectors, both with and without a linear trend in the non-stationary part of the process are derived. Then estimates and tests under linear restrictions on the cointegration vectors and their weights are given. The methods are illustrated by data from the Danish and the Finnish economy on the demand for money.