On the distribution of tests of cointegration rank.

This paper analyses the likelihood test for the hypothesis of reduced cointegration rank in a Gaussian vector autoregressive model. In finite samples the rejection probability for the hypothesis may be quite different from the promised asymptotic size. An explained is found in the fact that the test is not similar. A new asymptotic distribution which depends continuously on the nuisance parameters is suggested. This captures the functional form of the exact distribution and gives a rather good approximation. The idea is discussed for some low dimensional examples