Testing Stationarity in Small- and Medium-Sized Samples when Disturbances are Serially Correlated


  • The author would like to thank Anindya Banerjee, three anonymous referees, Tommy Andersson, David Edgerton, Thomas Elger, Klas Fregert, Rolf Larsson, Johan Lyhagen, Joakim Westerlund and seminar participants at the Department of Economics, Lund University, for useful suggestions and discussions on the topics covered in, and relating to, this paper. The simulations in the current paper were carried out in Gauss on the LUNARC cluster. The author acknowledges valuable technical support from Lars M Johansson. Financial support, from The Crafoord Foundation, The Royal Swedish Academy of Sciences and The Jan Wallander and Tom Hedelius Foundation, research grant number P2005-0117:1, is gratefully acknowledged. The views expressed in this paper are solely the responsibility of the author and should not to be interpreted as reflecting the views of the Executive Board of Sveriges Riksbank.


In this article, we study the size distortions of the KPSS test for stationarity when serial correlation is present and samples are small- and medium-sized. It is argued that two distinct sources of the size distortions can be identified. The first source is the finite-sample distribution of the long-run variance estimator used in the KPSS test, while the second source of the size distortions is the serial correlation not captured by the long-run variance estimator because of a too narrow choice of truncation lag parameter. When the relative importance of the two sources is studied, it is found that the size of the KPSS test can be reasonably well controlled if the finite-sample distribution of the KPSS test statistic, conditional on the time-series dimension and the truncation lag parameter, is used. Hence, finite-sample critical values, which can be applied to reduce the size distortions of the KPSS test, are supplied. When the power of the test is studied, it is found that the price paid for the increased size control is a lower raw power against a non-stationary alternative hypothesis.