Modified tests for a change in persistence

In this paper we propose a set of new persistence change tests which are based on modified versions of the ratio-based statistics of Kim [2000. Detection of change in persistence of a linear time series. Journal of Econometrics 95, 97–116], Kim et al. [2002. Corrigendum to “Detection of change in persistence of a linear time series”. Journal of Econometrics 109, 389–392] and Busetti and Taylor [2004. Tests of stationarity against a change in persistence. Journal of Econometrics 123, 33–66]. These 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 from trend stationarity to difference stationarity ( I ( 1 ) ) , or vice versa. We demonstrate that the existing tests are unable to adequately discern between a change in persistence and a constant I ( 1 ) process. Our proposed modifications, which involve the use of variable addition (pseudo-) statistics as scale factors, yield tests which, by design, have the same critical values regardless of whether the process is I ( 0 ) or (near) I ( 1 ) throughout. Hence, our null hypothesis is that of constant persistence (either constant I ( 0 ) or constant I ( 1 ) ). Tests directed against both I ( 1 ) to I ( 0 ) and I ( 0 ) to I ( 1 ) persistence change series are considered, together with tests where the direction of change under the alternative is unspecified. Our modified tests retain the same rates of consistency against persistence change processes as their unmodified counterparts. Numerical evidence suggests that our procedures work well in practice, with the modified ratio-based tests approximately correctly sized under both constant I ( 0 ) and constant (near) I ( 1 ) environments, and in most cases remaining competitive on power against persistence change processes, relative to the unmodified tests.