A robust version of the KPSS test based on ranks Matteo M. Pelagatti a,∗ , Pranab K. Sen b a Department of Statistics, Universit` a degli Studi di Milano-Bicocca, Via Bicocca degli Arcimboldi 8, 20126 Milan, Italy b Department of Statistics and Operations Research, University of North Carolina, 318 Hanes Hall, Chapel Hill, NC 27599-3260 Abstract This paper proposes a test of the null hypothesis of stationarity that is robust to the presence of fat-tailed errors. The test statistic is a modified version of the KPSS statistic, in which ranks substitute the original observations. The rank KPSS statistic has the same limiting distribution as the standard KPSS statistic under the null and diverges under I(1) alternatives. It features good power both under thin-tailed and fat-tailed distributions and it turns out to be a valid alternative to the original KPSS and the recently proposed Index KPSS (de Jong et al., 2007). Key words: Stationarity testing, Time series, Robustness, Empirical processes, Rank statistics JEL classification: C12; C14; C22 1. Introduction In a recent paper de Jong et al. (2007) proposed a test of (level) station- arity robust to fat tailed processes. Their test is based on the KPSS statistic of Kwiatkowski et al. (1992) applied to the signs of median-centered obser- vations, and therefore the existence of moments is not required, while the asymptotic distribution under the null is the same as that of the KPSS statistic. ∗ Corresponding author (Tel +39-02-64485834, Fax +39-02-64485878). The first author wishes to thank the University of Milan-Bicocca for a FAR2008 grant and the MURST for a PRIN2007 grant. We both thank Robert de Jong for providing us with the data used in de Jong et al. (2007). Email addresses: matteo.pelagatti@unimib.it (Matteo M. Pelagatti), pksen@bios.unc.edu (Pranab K. Sen) Preprint submitted to Elsevier July 15, 2009