On the finite sample size and power of the generalized KPSS test in the presence of level breaks

The KPSS stationarity test is oversized when it is applied to a series containing a strong autoregressive process. Hobijn et al. (2004) demonstrated that the test appears to be better-sized when an automatic-data dependent bandwidth selection procedure is used to estimate the long-run variance of the series. This article examines the impact of level breaks under the null on the finite sample size and power of their generalized KPSS test. It demonstrates that empirical sizes depend critically on the location and the magnitude of the break and that the generalized test is not as robust to variance estimation as was previously thought. The results are shown to be similar to those based on the traditional approach to calculating the KPSS test.