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Testing for (in)finite moments

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  • Trapani, Lorenzo

Abstract

This paper proposes a test to verify whether the kth moment of a random variable is finite. We use the fact that, under general assumptions, sample moments either converge to a finite number or diverge to infinity according as the corresponding population moment is finite or not. Building on this, we propose a test for the null that the kth moment does not exist. Since, by construction, our test statistic diverges under the null and converges under the alternative, we propose a randomised testing procedure to discern between the two cases. We study the application of the test to raw data, and to regression residuals. Monte Carlo evidence shows that the test has the correct size and good power; the results are further illustrated through an application to financial data.

Suggested Citation

  • Trapani, Lorenzo, 2016. "Testing for (in)finite moments," Journal of Econometrics, Elsevier, vol. 191(1), pages 57-68.
  • Handle: RePEc:eee:econom:v:191:y:2016:i:1:p:57-68
    DOI: 10.1016/j.jeconom.2015.08.006
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    References listed on IDEAS

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    1. Fedotenkov, Igor, 2015. "A simple nonparametric test for the existence of finite moments," MPRA Paper 66089, University Library of Munich, Germany.
    2. Loretan, Mico & Phillips, Peter C. B., 1994. "Testing the covariance stationarity of heavy-tailed time series: An overview of the theory with applications to several financial datasets," Journal of Empirical Finance, Elsevier, vol. 1(2), pages 211-248, January.
    3. Bandi, Federico M. & Corradi, Valentina, 2014. "Nonparametric Nonstationarity Tests," Econometric Theory, Cambridge University Press, vol. 30(01), pages 127-149, February.
    4. 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.
    5. Corradi, Valentina & Swanson, Norman R., 2006. "The effect of data transformation on common cycle, cointegration, and unit root tests: Monte Carlo results and a simple test," Journal of Econometrics, Elsevier, vol. 132(1), pages 195-229, May.
    6. Markowitz, Harry M & Usmen, Nilufer, 1996. "The Likelihood of Various Stock Market Return Distributions, Part 1: Principles of Inference," Journal of Risk and Uncertainty, Springer, vol. 13(3), pages 207-219, November.
    7. Drees, Holger & Kaufmann, Edgar, 1998. "Selecting the optimal sample fraction in univariate extreme value estimation," Stochastic Processes and their Applications, Elsevier, vol. 75(2), pages 149-172, July.
    8. Cornea-Madeira, Adriana & Davidson, Russell, 2015. "A Parametric Bootstrap For Heavy-Tailed Distributions," Econometric Theory, Cambridge University Press, vol. 31(03), pages 449-470, June.
    9. Markowitz, Harry M & Usmen, Nilufer, 1996. "The Likelihood of Various Stock Market Return Distributions, Part 2: Empirical Results," Journal of Risk and Uncertainty, Springer, vol. 13(3), pages 221-247, November.
    10. Hill, Jonathan B., 2010. "On Tail Index Estimation For Dependent, Heterogeneous Data," Econometric Theory, Cambridge University Press, vol. 26(05), pages 1398-1436, October.
    11. Phillips, Peter C. B. & Loretan, Mico, 1991. "The Durbin-Watson ratio under infinite-variance errors," Journal of Econometrics, Elsevier, vol. 47(1), pages 85-114, January.
    12. Linton, Oliver & Xiao, Zhijie, 2013. "Estimation Of And Inference About The Expected Shortfall For Time Series With Infinite Variance," Econometric Theory, Cambridge University Press, vol. 29(04), pages 771-807, August.
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    Cited by:

    1. Matteo Barigozzi & Lorenzo Trapani, 2017. "Sequential testing for structural stability in approximate factor models," Papers 1708.02786, arXiv.org, revised Mar 2018.
    2. repec:eee:econom:v:202:y:2018:i:1:p:1-17 is not listed on IDEAS

    More about this item

    Keywords

    Finite moments; Randomised tests; Chover-type Law of the Iterated Logarithm; Strong Law of Large Numbers;

    JEL classification:

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

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