Tests of stationarity against a change in persistence

Abstract

This paper considers testing against a change in the order of integration of a time series, either from I(0) to I(1) or from I(1) to I(0), at some known or unknown point in the sample. The null hypothesis is that the series is stochastically stationary around a deterministic trend function. For the case of a known change-point the locally best invariant (LBI) tests against the above changes in the order of integration are derived under the assumption of Gaussianity. When the change-point is not known we construct our tests taking functions of the LBI statistics over all possible break-dates. Sub-sample implementations of existing stationarity tests are also considered. We demonstrate by a series of simulation experiments that, for a given direction of change, the LBI-based approach can deliver considerably more powerful tests than both the sub-sample stationarity tests and the ratio-based tests of Kim et al. (J. Econom. 109 (2002) 389) and Busetti and Taylor (Tests of stationarity against a change in persistence, University of Birmingham, Department of Economics, Discussion Paper 01-13, 2001). Moreover, the power losses from an unknown breakpoint do not appear to be large. We also find that standard stationarity tests have good power against both changes from I(0) to I(1) and vice versa, while the ratio-based tests are consistent only against a known direction of change. A further test constructed in terms of the LBI-based statistics for the two possible directions of change is shown to perform generally better than the standard stationarity tests when the direction of change under the alternative is not known. Finally, we apply the tests discussed in the paper to the US inflation rate and find evidence for a change in persistence from I(1) to I(0) behaviour although, significantly, the timing of this change varies according to whether or not a simultaneous change in the level of the series is allowed.