A Note on Testing Covariance Stationarity
指出Xiao和Lima（2007）关于波动率线性趋势下KPSS检验功效接近检验水平的发现并不普遍成立，并提出了改进的协方差平稳性检验方法。
In a recent article, Xiao and Lima (2007 Xiao , Z. , Lima , L. R. ( 2007 ). Testing covariance stationarity . Econometric Reviews 26 : 643 – 667 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) show numerically that the stationarity test of Kwiatkowski et al. (1992 Kwiatkowski , D. , Phillips , P. C. B. , Schmidt , P. , Shin , Y. ( 1992 ). Testing the null hypothesis of stationarity against the alternative of a unit root: how sure are we that economic time series have a unit root? J. Econometrics 54 : 159 – 178 .[Crossref], [Web of Science ®] , [Google Scholar]) has power close to size when the volatility of the innovation process follows a linear trend. In this article, highlighting published results in Cavaliere and Taylor (2005 Cavaliere , G. , Taylor , A. M. R. ( 2005 ). Stationarity tests under time-varying second moments . Econometric Theory 21 : 1112 – 1129 .[Crossref], [Web of Science ®] , [Google Scholar]), we show that this observation does not in general hold under time-varying volatility. We also propose alternative tests of covariance stationarity which we show to improve upon the power properties of the tests proposed in Xiao and Lima (2007 Xiao , Z. , Lima , L. R. ( 2007 ). Testing covariance stationarity . Econometric Reviews 26 : 643 – 667 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) against changes in the unconditional variance. Practical recommendations are also made.