Abstract
This article considers simple least squares based unit root tests in time series models accommodating nonlinear trends and time-varying deepness and steepness in the dynamic law. The unit root tests are applied to 214 U.S. post-war macroeconomic time series (the same data set as in Stock and Watson, 1999 and Lundbergh, Teräsvirta, and van Dijk, 2003), and the overall rejection rate allowing for a linear (nonlinear) trend specification is 50% (67%). The highest rejection rate by an individual test is 40% (53%) and it arises from a time-varying steepness model. The lowest rejection rate of an individual test is the one by the ADF test and equals 12% (19%).The steps of unit root testing and model building are illustrated in more detail for U.S. unemployment rates. The unit root hypothesis is rejected for this series, and successive specification tests and estimation results yield evidence in favor of a stable TV-MSTAR model with more momentum in unemployments increases than in unemployment decreases.