On unit-root tests when the alternative is a trend-break stationary process

Minimum t statistics to test for a unit-root are available when the form of break under the alternative evolves according to the crash, changing growth, and mixed models. It is shown that serious power distortions occur if the form of break is misspecified, and thus the practitioner should use the mixed model as the appropriate alternative in empirical applications. The mixed model may reveal useful information regarding the location and form of break. The maximum F statistic for the joint null of a unit-root and no breaks is shown to have greater and less erratic power compared to the minimum t statistic. Stronger evidence against the unit-root is found for the Nelson-Plosser series and U.S. Postwar quarterly real gross national product.