On the Size Properties of Phillips–Perron Tests

The unit root tests of Phillips and Perron (Testing for a unit root in time series regression. Biometrika 75 (1988), 335–46) are frequently employed in applied econometric research. The chief attraction of these tests is that they are non-parametric, so it is unnecessary to specify a model, even as an approximation to the underlying generating process. The continued popularity of these tests is perhaps surprising since, beginning with Schwert (Tests for unit roots: a Monte Carlo investigation. J. Bus. Econ. Stat. 7 (1989), 147–59), simulation evidence has frequently suggested severe size distortions in specific low persistence generating models. It has been assumed that this size distortion is due to the requirement to estimate short- and long-run variances in practical implementation of the tests, and various alternative estimators have been analysed. However, the analysis of this paper suggests that part of the cause of the size distortion is more fundamental. Even in the 'idealistic case' where actual values of the true variances are used, serious size distortions remain for two simple generating models in sample sizes common in economic applications. We explore in detail the sources of this phenomenon for the ARIMA(0, 1, 1) generating model.