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A KPSS better than KPSS. Rank tests for short memory stationarity

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  • Matteo Pelagatti

    ()
    (Department of Statistics, Università degli Studi di Milano-Bicocca)

  • Pranab Sen

    (Department of Statistics and Operations Research, University of North Carolina at Chapel Hill)

Abstract

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 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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File URL: http://www.statistica.unimib.it/utenti/WorkingPapers/WorkingPapers/20110201.pdf
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Bibliographic Info

Paper provided by Università degli Studi di Milano-Bicocca, Dipartimento di Statistica in its series Working Papers with number 20110201.

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Length: 44 pages
Date of creation: Oct 2010
Date of revision:
Handle: RePEc:mis:wpaper:20110201

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Keywords: Stationarity test; Unit roots; Robustness; Rank statistics; Theil-Sen estimator; Asymptotic efficiency;

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  1. de Jong, Robert M. & Amsler, Christine & Schmidt, Peter, 2007. "A robust version of the KPSS test based on indicators," Journal of Econometrics, Elsevier, vol. 137(2), pages 311-333, April.
  2. Jong, R.M. de & Davidson, J., 1996. "Consistency of Kernel Estimators of Heteroscedastic and Autocorrelated Covariance Matrices," Discussion Paper 1996-52, Tilburg University, Center for Economic Research.
  3. De Vany, Arthur S. & Walls, W. David, 1999. "Cointegration analysis of spot electricity prices: insights on transmission efficiency in the western US," Energy Economics, Elsevier, vol. 21(5), pages 435-448, October.
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