Finite Sample Performance of Likelihood Ratio Tests for Cointegrating Ranks in Vector Autoregressions

This paper investigates through Monte Carlo simulation the finite sample properties of likelihood ratio tests for cointegrating ranks that were proposed by Johansen (1991, <italic>Econometrica</italic> 59, 1551–1580). We transform the model into a canonical form so that the experiment is well controlled without loss of generality and then conduct a comprehensive simulation study. As expected, the test performance is very sensitive to the value of the stationary root(s) of the process. We also find that the test performance depends crucially on the correlation between the innovations that drive the stationary and the nonstationary components of the process. We conclude that 100 observations are not sufficient to ensure reasonably good performance uniformly over the values of the nuisance parameters that affect the distributions of the test statistics.