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A bootstrap method to test for the existence of finite moments

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  • Igor Fedotenkov

Abstract

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

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    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. 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.
    3. R. Cont, 2001. "Empirical properties of asset returns: stylized facts and statistical issues," Quantitative Finance, Taylor & Francis Journals, vol. 1(2), pages 223-236.
    4. Benoit Mandelbrot, 2015. "The Variation of Certain Speculative Prices," World Scientific Book Chapters, in: Anastasios G Malliaris & William T Ziemba (ed.), 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. Wai Leong Ng & Chun Yip Yau, 2018. "Test for the existence of finite moments via bootstrap," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 30(1), pages 28-48, January.
    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. Degiannakis, Stavros & Filis, George & Siourounis, Grigorios & Trapani, Lorenzo, 2019. "Superkurtosis," MPRA Paper 94473, University Library of Munich, Germany.
      • Degiannakis, Stavros & Filis, George & Siourounis, Grigorios & Trapani, Lorenzo, 2019. "Superkurtosis," MPRA Paper 96563, University Library of Munich, Germany.
    5. Fedotenkov, Igor, 2015. "A simple nonparametric test for the existence of finite moments," MPRA Paper 66089, University Library of Munich, Germany.
    6. 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.
    7. Rafael Bernardo Carmona-Benítez & María Rosa Nieto, 2017. "Comparison of bootstrap estimation intervals to forecast arithmetic mean and median air passenger demand," Journal of Applied Statistics, Taylor & Francis Journals, vol. 44(7), pages 1211-1224, May.
    8. 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.
    9. Dewitte, Ruben, 2020. "From Heavy-Tailed Micro to Macro: on the characterization of firm-level heterogeneity and its aggregation properties," MPRA Paper 103170, University Library of Munich, Germany.

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