Rank tests for short memory stationarity

We propose a rank-test of the null hypothesis of short memory stationarity possibly after linear detrending. For the level-stationarity hypothesis, the test statistic we propose is a modified version of the popular KPSS statistic, in which ranks substitute the original observations. We prove that the rank KPSS statistic shares the same limiting distribution as the standard KPSS statistic under the null and diverges under I(1) alternatives. For the trend-stationarity hypothesis, we apply the same rank KPSS statistic to the residuals of a Theil–Sen regression on a linear trend. We derive the asymptotic distribution of the Theil–Sen estimator under short memory errors and prove that the Theil–Sen detrended rank KPSS statistic shares the same weak limit as the least-squares detrended KPSS. We study the asymptotic relative efficiency of our test compared to the KPSS and prove that it may have unbounded efficiency gains under fat-tailed distributions compensated by very moderate efficiency losses under thin-tailed distributions. For this and other reasons discussed in the body of the article our rank KPSS test turns out to be a valuable alternative to the KPSS for most real-world economic and financial applications. The weak convergence results and asymptotic representations proved in this article should interest a wider audience than that concerned with stationarity testing, as they extend to ranks analogous invariance principles widely used in unit-root econometrics