Tests for the stationarity null due to Kwiatkowski et al. (1992) has been an indispensable part of tool kits for empirical time series research. The tests however display considerable size distortions in the presence of highly persistent but stationary processes. Using a localto-unity framework, the paper offers an asymptotic explanation why the size problem comes into existence. The analysis shows that the tests fail to converge without a renormalization in the parameter space of concern. But it lends limited practical modifications to reducing the size bias, because of an unknown local-to-unity parameter that cannot be consistently estimated. We devise a parametric bootstrap scheme to account for the size distortions instead. Our bootstrap proposal is able to generate independent bootstrap re-samples, regardless of the dependence in the component representation of the considered series. Even in the problematic parameter space, simulations demonstrate that our bootstrap tests exhibit an excellent control over the empirical rejection probabilities, while maintaining a comparable power to the asymptotic counterparts, for both small and moderate sample sizes found in applications.
Discussion Papers NO50 Helsinki Center of Economic Research