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A note on the bootstrap method for testing the existence of finite moments

Author

Listed:
  • Igor Fedotenkov

    (Lithuanian Institute of Agrarian Economics, Vilnius - Ltuania)

Abstract

This paper discusses a bootstrap-based test, which checks if finite moments exist, and indicates cases of possible misapplication. It notes, that a procedure for finding the smallest power to which observations need to be raised, such that the test rejects a hypothesis that the corresponding moment is finite, works poorly as an estimator of the tail index or moment estimator. This is the case especially for very low- and high-order moments. Several examples of correct usage of the test are also shown. The main result is derived analytically, and a Monte-Carlo experiment is presented.

Suggested Citation

  • 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.
    • Handle: RePEc:bot:rivsta:v:74:y:2014:i:4:p:447-453
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    File URL: http://rivista-statistica.unibo.it/article/view/5504
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    References listed on IDEAS

    as
    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.
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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. Robin Merkle & Andrea Barth, 2022. "On Some Distributional Properties of Subordinated Gaussian Random Fields," Methodology and Computing in Applied Probability, Springer, vol. 24(4), pages 2661-2688, December.
    3. 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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    More about this item

    Keywords

    Bootstrap; finite moments; heavy tails; tail index estimator; test;
    All these keywords.

    JEL classification:

    • C00 - Mathematical and Quantitative Methods - - General - - - General
    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General

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