Testing for a Unit Root in the Presence of a Maintained Trend

Abstract

This paper develops statistics for detecting the presence of a unit root in time series data against the alternative of stationarity. Unlike most existing procedures, the new tests allow for deterministic trend polynomials in the maintained hypothesis. They may be used to discriminate between unit root nonstationarity and processes which are stationary around a deterministic polynomial trend. The tests allow for both forms of nonstationarity under the null hypothesis. Moreover, the tests allow for a wide class of weakly dependent and possibly heterogenously distributed errors. We illustrate the use of the new tests by applying them to a number of models of macroeconomic behavior.