On tests for changes in persistence

There is mounting evidence that the parameters of autoregressive models fitted to many economic and financial time-series are unstable across time, often displaying changes in persistence between I(0) and I(1) behaviour. See, inter alia, Stock and Watson [J. Business Econ. Stat. 14 (1996) 11] and Garcia and Perron [Rev. Econ. Stat. 78 (1996) 111]. Tests for changes in persistence have recently been developed in Kim [J. Econ. 95 (2000) 97], based on ratio statistics which require no modifications for weak dependence in the driving shocks to facilitate asymptotically pivotal inference. However, the tests can be very badly over-sized against weakly dependent processes in finite samples, as we show in this paper. We propose simple modifications of these ratio statistics, which have the same (pivotal) limiting null distributions as the unmodified statistics but yield tests with much improved finite sample size properties under weakly dependent shocks.