Wald Tests For Detecting Multiple Structural Changes In Persistence

This paper considers the problem of testing for multiple structural changes in the persistence of a univariate time series. We propose sup-Wald tests of the null hypothesis that the process has an autoregressive unit root throughout the sample against the alternative hypothesis that the process alternates between stationary and unit root regimes. We derive the limit distributions of the tests under the null and establish their consistency under the relevant alternatives. We further show that the tests are inconsistent when directed against the incorrect alternative, thereby enabling identification of the nature of persistence in the initial regime. We also propose hybrid testing procedures that allow ruling out of stable stationary processes or ones that are subject to only stationary changes under the null, thereby aiding the researcher in interpreting a rejection as emanating from a switch between a unit root and stationary regime. The computation of the test statistics as well as asymptotic critical values is facilitated by the dynamic programming algorithm proposed in Perron and Qu (2006, Journal of Econometrics134, 373–399) which allows imposing within- and cross-regime restrictions on the parameters. Finally, we present Monte Carlo evidence to show that the proposed procedures perform well in finite samples relative to those available in the literature.