On the Use of Sub-Sample Unit Root Tests to Detect Changes in Persistence

We investigate the behaviour of rolling and recursive augmented Dickey-Fuller (ADF) tests against processes which display changes in persistence. We show that the power of the tests depend crucially on the window width and warm up parameter for the rolling and recursive procedures respectively, on whether forward or reverse recursive sequences of tests are computed, and on the persistence change process generating the data. To ameliorate these dependencies we extend the available critical values for these tests, and propose a number of new sub-sample unit root tests for which finite sample and asymptotic critical values are also provided. An empirical illustration on OECD real output data is also provided