On the power of the KPSS test of stationarity against fractionally-integrated alternatives

Kwiatkowski, Phillips, Schmidt, and Shin (KPSS) proposed a test of the null hypothesis of stationarity. However, their distribution theory under the null hypothesis assumes that the series in question has short memory; that is, its partial sum satisfies an invariance principle. This paper shows that the KPSS test is consistent against stationary long memory alternatives, such as I(d) processes for d ϵ (−12, 12, d ≠ 0. It can therefore be used to distinguish short memory and long memory stationary processes. The power of the KPSS test in finite samples is found to be comparable to that of Loʹs modified rescaled range test. The results show that a rather large sample size, such as T = 1000, will be necessary to distinguish reliably between a long memory process and a short memory process with comparable short-term autocorrelation.