Selecting the lag length for the M ^GLS unit root tests with structural change: A warning note for practitioners based on simulations

This is a simulation-based warning note for practitioners who use the M ^GLS unit root tests in the context of structural change using different selection lag length criteria. With T = 100, we find severe oversize problems when using some criteria, while other criteria produce an undersizing behavior. In view of this dilemma, we do not recommend using these tests. While such behavior tends to disappear when T = 250, it is important to note that most empirical applications use smaller sample sizes such as T = 100 or T = 150. The ADF ^GLS test does not present an oversizing or undersizing problem. The only disadvantage of the ADF ^GLS test arises in the presence of MA(1) negative correlation, in which case the M ^GLS tests are preferable, but in all other cases they are very undersized. When there is a break in the series, selecting the breakpoint using the Supremum method greatly improves the results relative to the Infimum method.