A Test of Cointegration Rank Based on Principal Component Analysis (revised, January 2006)

This paper considers a test of the rank of cointegration. The test is based on the fact that in an m-variate system the m-r th principal component is I (1) under the null of r cointegration rank but I (0) under the alternative of r+1 cointegration rank. Exploiting this fact, we construct a cointegration rank test that is less restrictive than Johansen's tests, easy to calculate, and independent of the dimension of the process. Monte Carlo simulations indicate that the proposed test outperforms Johansen's tests, even in the case of a model that satisfies the assumptions required for Johansen's tests and when the sample size is small.