System estimators of cointegrating matrix in absence of normalising information

Of those system methods that do not require information regarding normalisation of cointegrating vectors, only the likelihood ratio test of Johansen is available for testing linear restrictions on the cointegrating matrix of the Gaussian VAR process. This paper considers system estimators, which are produced by the conventional canonical correlation analysis, for a class of rather general cointegrated processes. It is shown that such system estimators can be modified to achieve asymptotic efficiency. A Wald-like test for linear restrictions on the cointegrating matrix is proposed and shown to be asymptotically X2-distributed under the null hypothesis. The proposed estimators and test can be used to analyse non-VAR cointegrated processes.