Efficient and near efficient unit root tests in models with structural change

If a time series undergoes a structural change either in the form of a change in the mean of the series, a level shift, or in the form of a change in the growth rate of the series, a trend shift, unit root tests incorrectly fail to reject the null hypothesis of a unit root, if the effects of structural change is not taken into account. In this study, properties of unit root tests and the estimators of the deterministic component are examined using extensive Monte Carlo simulations. Further, this study develops new tests for the null hypothesis of a unit root against shifting trend stationary alternatives. In particular, models with structural change in the form of level or trend shifts are studied. Roots local-to-unity are addressed in models with structural change and asymptotic power functions of the tests are derived using local-to-unity asymptotic framework. These tests have good power properties against shifting trend stationary alternatives. Tests in the presence of multiple shifts are also examined. The asymptotic distributions of the tests are derived under exogenous and endogenous shift point assumptions. The asymptotic and finite sample percentiles of the tests are tabulated using Monte Carlo integration. Monte Carlo simulations reveal that tests have good power and size properties against various alternatives.;It is shown that the limiting distributions of the test statistics do not depend on the time of the shift for the level shift model. For the level shift model, the invariance of the tests to the shift point is also maintained in case of multiple shifts. Further, when the assumption of instantaneous response to level shifts is relaxed tests are still invariant to the shift point. For the trend shift model, the limiting distributions of the test statistics depend on the shift point. Therefore, the tests have less power against trend shift alternatives compared to level shift alternatives. Using these test statistics, we found that the conclusions of previous studies about some major US macroeconomic time series are mostly reversed and many of these series can be classified as unit root processes.