Testing for Multiple Structural Changes in Cointegrated Regression Models

We consider testing for multiple structural changes in cointegrated systems and 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. We also propose a sequential procedure that 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 nonmonotonic power in the presence of serial correlation in the errors.