This paper analyses the likelihood test for the hypothesis of reduced cointegration rank in a Gaussian vector autorgressive model. In finite samples the rejection probability for the hypothesis may be quite different from the promised asymptotic size. This is explained by the lack of similarity properties which arise as the analysis combines canonical correlation and autoregressive methods. In both cases tests are often non-similar. It is concluded that the test for cointegration rank cannot provide particularly strong evidence for the rank. Some alternative graphical diagnostics are therefore discussed.