Testing Stationarity in Small- and Medium-Sized Samples when Disturbances are Serially Correlated*
研究了KPSS平稳性检验在中小样本且存在序列相关时的规模扭曲，识别了两个扭曲来源，并提供了有限样本临界值以控制规模，同时分析了检验功效的损失。
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.