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 against the alternative hypothesis that the process alternates between stationary and unit root regimes. Both non-trending and trending cases are analyzed. We derive the limit distributions of the tests under the null and establish their consistency under the relevant alternatives. 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) which allows the minimization of the sum of squared residuals under the alternative hypothesis while imposing within and cross regime restrictions on the parameters. Finally, we present Monte Carlo evidence to show that the proposed tests perform quite well in finite samples relative to those available in the literature.