Residuals-based Tests for Cointegration: An Analytical Comparison

This paper compares five residuals-based tests for the null of no cointegration to identify which unit root test should be used when testing for cointegration. The tests are compared in terms of power and size distortions. The asymptotic distribution of the tests under the local alternative is shown to be a function of Brownian Motions and Ornstein-Uhlenbeck processes, depending on a single nuisance parameter, which is, determined by the correlation at frequency zero of the independent variables with the errors of the cointegration regression. It is shown that no significant improvement can be achieved by using different unit root tests than the t-test originally proposed by Engle and Granger (1987).