IDEAS home Printed from https://ideas.repec.org/a/eee/econom/v191y2016i1p57-68.html
   My bibliography  Save this article

Testing for (in)finite moments

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304407615002596
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jeconom.2015.08.006?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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(1), 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(3), 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. 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.
    11. Hill, Jonathan B., 2010. "On Tail Index Estimation For Dependent, Heterogeneous Data," Econometric Theory, Cambridge University Press, vol. 26(5), pages 1398-1436, October.
    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(4), pages 771-807, August.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Pan, Ging-Ginq & Shiu, Yung-Ming & Wu, Tu-Cheng, 2024. "Extrapolation and option-implied kurtosis in volatility forecasting," Pacific-Basin Finance Journal, Elsevier, vol. 84(C).
    2. Yang, Jangho & Heinrich, Torsten & Winkler, Julian & Lafond, François & Koutroumpis, Pantelis & Farmer, J. Doyne, 2019. "Measuring productivity dispersion: a parametric approach using the Lévy alpha-stable distribution," MPRA Paper 96474, University Library of Munich, Germany.
    3. Matteo Barigozzi & Giuseppe Cavaliere & Lorenzo Trapani, 2024. "Inference in Heavy-Tailed Nonstationary Multivariate Time Series," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 119(545), pages 565-581, January.
    4. Stavros Degiannakis & George Filis & Grigorios Siourounis & Lorenzo Trapani, 2023. "Superkurtosis," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 55(8), pages 2061-2091, December.
      • Degiannakis, Stavros & Filis, George & Siourounis, Grigorios & Trapani, Lorenzo, 2019. "Superkurtosis," MPRA Paper 94473, University Library of Munich, Germany.
      • Stavros Degiannakis & George Filis & Grigorios Siourounis & Lorenzo Trapani, 2023. "Superkurtosis," Working Papers 318, Bank of Greece.
      • Degiannakis, Stavros & Filis, George & Siourounis, Grigorios & Trapani, Lorenzo, 2019. "Superkurtosis," MPRA Paper 96563, University Library of Munich, Germany.
    5. Barigozzi, Matteo & Trapani, Lorenzo, 2020. "Sequential testing for structural stability in approximate factor models," Stochastic Processes and their Applications, Elsevier, vol. 130(8), pages 5149-5187.
    6. Francq, Christian & Zakoian, Jean-Michel, 2024. "Finite moments testing in a general class of nonlinear time series models," MPRA Paper 121193, University Library of Munich, Germany.
    7. Francq, Christian & Zakoïan, Jean-Michel, 2022. "Testing the existence of moments for GARCH processes," Journal of Econometrics, Elsevier, vol. 227(1), pages 47-64.
    8. Lorenzo Trapani & Emily Whitehouse, 2020. "Sequential monitoring for cointegrating regressions," Papers 2003.12182, arXiv.org.
    9. Francq, Christian & Zakoian, Jean-Michel, 2021. "Testing the existence of moments and estimating the tail index of augmented garch processes," MPRA Paper 110511, University Library of Munich, Germany.
    10. Ahmadreza Marandi & Aharon Ben-Tal & Dick den Hertog & Bertrand Melenberg, 2022. "Extending the Scope of Robust Quadratic Optimization," INFORMS Journal on Computing, INFORMS, vol. 34(1), pages 211-226, January.
    11. Torsten Heinrich & Jangho Yang & Shuanping Dai, 2020. "Levels of structural change: An analysis of China's development push 1998-2014," Papers 2005.01882, arXiv.org, revised Sep 2020.
    12. Torsten Heinrich & Jangho Yang & Shuanping Dai, 2022. "Levels of structural change," Journal of Evolutionary Economics, Springer, vol. 32(1), pages 35-86, January.
    13. Cavaliere, Giuseppe & Mikosch, Thomas & Rahbek, Anders & Vilandt, Frederik, 2024. "Tail behavior of ACD models and consequences for likelihood-based estimation," Journal of Econometrics, Elsevier, vol. 238(2).
    14. Li, Dong & Zhang, Xingfa & Zhu, Ke & Ling, Shiqing, 2018. "The ZD-GARCH model: A new way to study heteroscedasticity," Journal of Econometrics, Elsevier, vol. 202(1), pages 1-17.
    15. Yang, Jangho & Heinrich, Torsten & Winkler, Julian & Lafond, François & Koutroumpis, Pantelis & Farmer, J. Doyne, 2019. "Measuring productivity dispersion: a parametric approach using the Lévy alpha-stable distribution," MPRA Paper 96474, University Library of Munich, Germany.
    16. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Hill, Jonathan B. & Aguilar, Mike, 2013. "Moment condition tests for heavy tailed time series," Journal of Econometrics, Elsevier, vol. 172(2), pages 255-274.
    2. Markowitz, Harry, 2014. "Mean–variance approximations to expected utility," European Journal of Operational Research, Elsevier, vol. 234(2), pages 346-355.
    3. Runde, Ralf & Scheffner, Axel, 1998. "On the existence of moments: With an application to German stock returns," Technical Reports 1998,25, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    4. Giorgio Fagiolo & Mauro Napoletano & Andrea Roventini, 2008. "Are output growth-rate distributions fat-tailed? some evidence from OECD countries," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 23(5), pages 639-669.
    5. Lorenzo Trapani, 2021. "Testing for strict stationarity in a random coefficient autoregressive model," Econometric Reviews, Taylor & Francis Journals, vol. 40(3), pages 220-256, April.
    6. Gagliardini, Patrick & Ossola, Elisa & Scaillet, Olivier, 2019. "A diagnostic criterion for approximate factor structure," Journal of Econometrics, Elsevier, vol. 212(2), pages 503-521.
    7. Kevin Fergusson & Eckhard Platen, 2006. "On the Distributional Characterization of Daily Log-Returns of a World Stock Index," Applied Mathematical Finance, Taylor & Francis Journals, vol. 13(1), pages 19-38.
    8. Fergusson, Kevin, 2020. "Less-Expensive Valuation And Reserving Of Long-Dated Variable Annuities When Interest Rates And Mortality Rates Are Stochastic," ASTIN Bulletin, Cambridge University Press, vol. 50(2), pages 381-417, May.
    9. Barigozzi, Matteo & Trapani, Lorenzo, 2020. "Sequential testing for structural stability in approximate factor models," Stochastic Processes and their Applications, Elsevier, vol. 130(8), pages 5149-5187.
    10. Kurz-Kim, Jeong-Ryeol & Loretan, Mico, 2014. "On the properties of the coefficient of determination in regression models with infinite variance variables," Journal of Econometrics, Elsevier, vol. 181(1), pages 15-24.
    11. repec:uts:finphd:40 is not listed on IDEAS
    12. Hill, Jonathan B. & Prokhorov, Artem, 2016. "GEL estimation for heavy-tailed GARCH models with robust empirical likelihood inference," Journal of Econometrics, Elsevier, vol. 190(1), pages 18-45.
    13. Matteo Barigozzi & Lorenzo Trapani, 2018. "Determining the dimension of factor structures in non-stationary large datasets," Papers 1806.03647, arXiv.org.
    14. Panayiotis Theodossiou, 1998. "Financial Data and the Skewed Generalized T Distribution," Management Science, INFORMS, vol. 44(12-Part-1), pages 1650-1661, December.
    15. Ghaffari, N. & Walker, S.G., 2023. "W2 barycenters for radially related distributions," Statistics & Probability Letters, Elsevier, vol. 195(C).
    16. Jiang, Chonghui & Ma, Yongkai & An, Yunbi, 2016. "Portfolio selection with a systematic skewness constraint," The North American Journal of Economics and Finance, Elsevier, vol. 37(C), pages 393-405.
    17. Carbajal-De-Nova, Carolina & Venegas-Martínez, Francisco, 2019. "On the paradigm shift of asset pricing models, before and after the global financial crisis: a literature review," Panorama Económico, Escuela Superior de Economía, Instituto Politécnico Nacional, vol. 15(29), pages 7-38, Primer se.
    18. Paulo M.M. Rodrigues & João Nicolau, 2015. "A New Regression-Based Tail Index Estimator: An Application to Exchange Rates," Working Papers w201514, Banco de Portugal, Economics and Research Department.
    19. Kevin John Fergusson, 2018. "Less-Expensive Pricing and Hedging of Extreme-Maturity Interest Rate Derivatives and Equity Index Options Under the Real-World Measure," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 3-2018, January-A.
    20. 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.
    21. Gagliardini, Patrick & Ossola, Elisa & Scaillet, Olivier, 2019. "Estimation of large dimensional conditional factor models in finance," Working Papers unige:125031, University of Geneva, Geneva School of Economics and Management.

    More about this item

    Keywords

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

    JEL classification:

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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:econom:v:191:y:2016:i:1:p:57-68. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/jeconom .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.