A Robust Sequential Procedure for Estimating the Number of Structural Changes in Persistence

This paper proposes a new procedure for estimating the number of structural changes in the persistence of a univariate time series. In contrast to the extant literature that primarily assumes (regime-wise) stationarity, our framework also allows the underlying stochastic process to switch between stationary [I(0)] and unit root [I(1)] regimes. We develop a sequential testing approach based on the simultaneous application of two Wald-type tests for structural change, one of which assumes the process is I(0)-stable under the null hypothesis while the other assumes the stable I(1) model as the null hypothesis. This feature allows the procedure to maintain correct asymptotic size regardless of whether the regimes are I(0) or I(1). We also propose a novel procedure for distinguishing processes with pure level and/or trend shifts from those that are also subject to concurrent shifts in persistence. The large sample properties of the recommended procedures are derived and the relevant asymptotic critical values tabulated. Our Monte Carlo experiments demonstrate that the advocated approach compares favorably relative to the commonly employed approach based on I(0) sequential testing, especially when the data contain an I(1) segment.