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A simple nonparametric test for the existence of finite moments

Listed author(s):
  • Fedotenkov, Igor

This paper proposes a simple, fast and direct nonparametric test to verify if a sample is drawn from a distribution with a finite first moment. The method can also be applied to test for the existence of finite moments of another order by taking the sample to the corresponding power. The test is based on the difference in the asymptotic behaviour of the arithmetic mean between cases when the underlying probability function either has or does not have a finite first moment. Test consistency is proved; then, test performance is illustrated with Monte-Carlo simulations and a practical application for the S&P500 index.

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File URL: https://mpra.ub.uni-muenchen.de/66089/1/MPRA_paper_66089.pdf
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Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 66089.

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Date of creation: 13 Aug 2015
Handle: RePEc:pra:mprapa:66089
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  1. Einmahl, J. H.J. & Dekkers, A. L.M. & de Haan, L., 1989. "A moment estimator for the index of an extreme-value distribution," Other publications TiSEM 81970cb3-5b7a-4cad-9bf6-2, Tilburg University, School of Economics and Management.
  2. Igor Fedotenkov, 2013. "A bootstrap method to test for the existence of finite moments," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 25(2), pages 315-322, June.
  3. Jansen, Dennis W & de Vries, Casper G, 1991. "On the Frequency of Large Stock Returns: Putting Booms and Busts into Perspective," The Review of Economics and Statistics, MIT Press, vol. 73(1), pages 18-24, February.
  4. Corradi, Valentina & Swanson, Norman R., 2002. "A consistent test for nonlinear out of sample predictive accuracy," Journal of Econometrics, Elsevier, vol. 110(2), pages 353-381, October.
  5. Pagan, Adrian, 1996. "The econometrics of financial markets," Journal of Empirical Finance, Elsevier, vol. 3(1), pages 15-102, May.
  6. R. Cont, 2001. "Empirical properties of asset returns: stylized facts and statistical issues," Quantitative Finance, Taylor & Francis Journals, vol. 1(2), pages 223-236.
  7. Benoit Mandelbrot, 2015. "The Variation of Certain Speculative Prices," World Scientific Book Chapters,in: THE WORLD SCIENTIFIC HANDBOOK OF FUTURES MARKETS, chapter 3, pages 39-78 World Scientific Publishing Co. Pte. Ltd..
  8. McNeil, Alexander J., 1997. "Estimating the Tails of Loss Severity Distributions Using Extreme Value Theory," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 27(01), pages 117-137, May.
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