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A bootstrap method to test for the existence of finite moments


  • Igor Fedotenkov


This paper presents a simple bootstrap test to verify the existence of finite moments. The efficacy of the test relies on the fact that in the absence of a first moment and under certain general conditions, the arithmetic average of a sample grows at a rate greater than the growth rates of the arithmetic averages of the sub-samples. Firstly, we show test consistency analytically. Then, Monte-Carlo simulations are performed to compare our test with the Hill estimator.

Suggested Citation

  • 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.
  • Handle: RePEc:taf:gnstxx:v:25:y:2013:i:2:p:315-322 DOI: 10.1080/10485252.2012.752487

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    References listed on IDEAS

    1. Danielsson, J. & de Haan, L. & Peng, L. & de Vries, C. G., 2001. "Using a Bootstrap Method to Choose the Sample Fraction in Tail Index Estimation," Journal of Multivariate Analysis, Elsevier, vol. 76(2), pages 226-248, February.
    2. R. Cont, 2001. "Empirical properties of asset returns: stylized facts and statistical issues," Quantitative Finance, Taylor & Francis Journals, vol. 1(2), pages 223-236.
    3. M. João Martins & M. Ivette Gopmes & M. Manuela Neves, 2004. "Averages of Hill estimators," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 13(1), pages 113-128, June.
    4. 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..
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    Cited by:

    1. Igor Fedotenkov, 2014. "A note on the bootstrap method for testing the existence of finite moments," Statistica, Department of Statistics, University of Bologna, vol. 74(4), pages 447-453.
    2. Trapani, Lorenzo, 2016. "Testing for (in)finite moments," Journal of Econometrics, Elsevier, vol. 191(1), pages 57-68.
    3. Alessandro Bucciol & Laura Cavalli & Igor Fedotenkov & Paolo Pertile & Veronica Polin & Nicola Sartor & Alessandro Sommacal, 2014. "A large scale OLG model for France, Italy and Sweden: assessing the interpersonal and intrapersonal redistributive effects of public policies," Working Papers 07/2014, University of Verona, Department of Economics.
    4. repec:taf:japsta:v:44:y:2017:i:7:p:1211-1224 is not listed on IDEAS
    5. Alexis Akira Toda & Kieran Walsh, 2015. "The Double Power Law in Consumption and Implications for Testing Euler Equations," Journal of Political Economy, University of Chicago Press, vol. 123(5), pages 1177-1200.
    6. Fedotenkov, Igor, 2015. "A simple nonparametric test for the existence of finite moments," MPRA Paper 66089, University Library of Munich, Germany.

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