A KPSS better than KPSS. Rank tests for short memory stationarity
AbstractWe 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 residual 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 an irresistible competitor of the KPSS for most real-world economic and financial applications. The weak convergence results and asymptotic representations proved in this article may have an interest on their own, as they extend to ranks analogous results widely used in unit-root econometrics.
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Bibliographic InfoPaper provided by Università degli Studi di Milano-Bicocca, Dipartimento di Statistica in its series Working Papers with number 20110201.
Length: 44 pages
Date of creation: Oct 2010
Date of revision:
Stationarity test; Unit roots; Robustness; Rank statistics; Theil-Sen estimator; Asymptotic efficiency;
Find related papers by JEL classification:
- C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
- C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
- C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models &bull Diffusion Processes
This paper has been announced in the following NEP Reports:
- NEP-ALL-2011-02-26 (All new papers)
- NEP-ECM-2011-02-26 (Econometrics)
- NEP-ETS-2011-02-26 (Econometric Time Series)
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