Detecting multiple changes in persistence

This paper considers the problem of testing for and dating changes (at unknown points) in the order of integration of a time series between different trend-stationary and difference-stationary regimes. While existing procedures in the literature are designed for processes displaying only a single such change in persistence, our proposed methodology is also valid in the presence of multiple changes in persistence. Our procedure is based on sequences of doubly-recursive implementations of the regression-based unit root statistic of Elliott et al. (1996). The asymptotic validity of our procedure is demonstrated analytically. We use Monte Carlo methods to simulate both finite sample and asymptotic critical values for our proposed testing procedure and to simulate the finite sample behaviour of our procedure against a variety of single and multiple persistence change series. The procedure is shown to work well in practice. The impact of deterministic level and trend breaks on our procedure is also discussed. An empirical application of the procedure to interest rate data is considered.