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. The authors propose sup-Wald tests of the null hypothesis that the process has an autoregressive unit root against the alternative hypothesis that the process alternates between stationary and unit root regimes. Both non-trending and trending cases are analyzed. They derive the limit distributions of the tests under the null and establish their consistency under the relevant alternatives.