Bartlett Corrections in Cointegration Testing

When testing for cointegration, the asymptotic inference typically in use can be plagued by size distortion due to an inadequate first order approximation. Hence, for practical purposes the inference can be completely misleading and result in false conclusions regarding the presence of long-run relationships in the data. Which, of course, in many applications is a key issue. We explore the potentials of Bartlett correction of two cointegration test statistics. The idea is to multiply the test statistic by a correcting factor derived from an asymptotic expansion of its expectation. As a consequence, the reference distribution should then provide a closer approximation to the resulting adjusted statistic in comparison with the unadjusted statistic. In a simple bivariate framework we derive a likelihood ratio test, as well as a first order approximation thereof, for testing the null hypothesis of no cointegration. Suitable Bartlett corrections for the two tests are suggested and using Monte Carlo simulation we evaluate the effectiveness of the proposed methods.