Unit roots and double smooth transitions

Techniques for testing the null hypothesis of difference stationarity against stationarity around some deterministic function have received much attention. In particular, unit root tests where the alternative is stationarity around a smooth transition in linear trend have recently been proposed to permit the possibility of non-instantaneous structural change. In this paper we extend such an approach to admit more than one structural change, allowing the model under the alternative hypothesis to be stationary about two smooth transitions in linear trend. Tests involving this added generality are developed and their properties investigated; application of the tests to two interesting time series highlights the potential benefits of this double transition extension.