Testing for a Change in Persistence in the Presence of a Volatility Shift

We consider the impact of a break in the innovation volatility process on ratio-based persistence change tests. We demonstrate that the ratio statistics used do not have pivotal limiting null distributions and that the associated tests display a considerable degree of size distortion with size approaching unity in some cases. In practice, therefore, on the basis of these tests the practitioner will face difficulty in discriminating between persistence change processes and processes which display a simple volatility break. A wild bootstrap-based solution to the identified inference problem is proposed and is shown to work well in practice.