A note on testing covariance stationarity

In a recent article, Xiao and Lima (2007) show numerically that the stationarity test of Kwiatkowski et al. (1992) 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), 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) against changes in the unconditional variance. Practical recommendations are also made.