Testing for Multiple Structural Changes in Cointegrated Regression Models

This paper considers issues related to testing for multiple structural changes in cointegrated systems. We derive the limiting distribution of the Sup-Wald test under mild conditions on the errors and regressors for a variety of testing problems. We show that even if the coefficients of the integrated regressors are held fixed but the intercept is allowed to change, the limit distributions are not the same as would prevail in a stationary framework. Including stationary regressors whose coefficients are not allowed to change does not affect the limiting distribution of the tests under the null hypothesis. We also propose a procedure that allows one to test the null hypothesis of, say, k changes, versus the alternative hypothesis of k + 1 changes. This sequential procedure is useful in that it permits consistent estimation of the number of breaks present. We show via simulations that our tests maintain the correct size in finite samples and are much more powerful than the commonly used LM tests, which suffer from important problems of non-monotonic power in the presence of serial correlation in the errors.