Fluctuation Tests for a Change in Persistence

In this paper, we develop a set of new persistence change tests which are similar in spirit to those of Kim [Journal of Econometrics (2000) Vol. 95, pp. 97-116], Kim et al. [Journal of Econometrics (2002) Vol. 109, pp. 389-392] and Busetti and Taylor [Journal of Econometrics (2004) Vol. 123, pp. 33-66]. While the exisiting tests are based on ratios of sub-sample Kwiatkowski et al. [Journal of Econometrics (1992) Vol. 54, pp. 158-179]-type statistics, our proposed tests are based on the corresponding functions of sub-sample implementations of the well-known maximal recursive-estimates and re-scaled range fluctuation statistics. Our statistics are used to test the null hypothesis that a time series displays constant trend stationarity [I(0)] behaviour against the alternative of a change in persistence either from trend stationarity to difference stationarity [I(1)], or vice versa. Representations for the limiting null distributions of the new statistics are derived and both finite-sample and asymptotic critical values are provided. The consistency of the tests against persistence change processes is also demonstrated. Numerical evidence suggests that our proposed tests provide a useful complement to the extant persistence change tests. An application of the tests to US inflation rate data is provided