Testing for a change in persistence in the presence of non-stationary volatility

In this paper we consider tests for the null of (trend-) stationarity against the alternative of a change in persistence at some (known or unknown) point in the observed sample, either from I(0) to I(1) behaviour or vice versa, of, inter alia, Kim (2000). We show that in circumstances where the innovation process displays non-stationary unconditional volatility of a very general form, which includes single and multiple volatility breaks as special cases, the ratiobased statistics used to test for persistence change do not have pivotal limiting null distributions. Numerical evidence suggests that this can cause severe oversizing in the tests. In practice it may therefore be hard to discriminate between persistence change processes and processes with constant persistence but which display time-varying unconditional volatility. We solve the identified inference problem by proposing wild bootstrap-based implementations of the tests. Monte Carlo evidence suggests that the bootstrap tests perform well in finite samples. An empirical application to a variety of measures of U.S. price inflation data is provided.