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)$I\left(0\right)$ to I(1)$I\left(1\right)$ behaviour or vice versa, of, inter alia, Kim, J., 2000. Detection of change in persistence of a linear time series. Journal of Econometrics 95, 97–116]. 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 ratio-based statistics used to test for persistence change do not have pivotal limiting null distributions. Numerical evidence suggests that this can cause severe over-sizing 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 illustration using US price inflation data is provided.