IDEAS home Printed from https://ideas.repec.org/a/spr/alstar/v106y2022i4d10.1007_s10182-022-00442-y.html
   My bibliography  Save this article

Some measures of kurtosis and their inference on large datasets

Author

Listed:
  • Claudio Giovanni Borroni

    (University of Milano-Bicocca)

  • Lucio De Capitani

    (University of Milano-Bicocca)

Abstract

This paper deals with the estimation of kurtosis on large datasets. It aims at overcoming two frequent limitations in applications: first, Pearson's standardized fourth moment is computed as a unique measure of kurtosis; second, the fact that data might be just samples is neglected, so that the opportunity of using suitable inferential tools, like standard errors and confidence intervals, is discarded. In the paper, some recent indexes of kurtosis are reviewed as alternatives to Pearson’s standardized fourth moment. The asymptotic distribution of their natural estimators is derived, and it is used as a tool to evaluate efficiency and to build confidence intervals. A simulation study is also conducted to provide practical indications about the choice of a suitable index. As a conclusion, researchers are warned against the use of classical Pearson’s index when the sample size is too low and/or the distribution is skewed and/or heavy-tailed. Specifically, the occurrence of heavy tails can deprive Pearson’s index of any meaning or produce unreliable confidence intervals. However, such limitations can be overcome by reverting to the reviewed alternative indexes, relying just on low-order moments.

Suggested Citation

  • Claudio Giovanni Borroni & Lucio De Capitani, 2022. "Some measures of kurtosis and their inference on large datasets," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 106(4), pages 573-607, December.
    • Handle: RePEc:spr:alstar:v:106:y:2022:i:4:d:10.1007_s10182-022-00442-y
    DOI: 10.1007/s10182-022-00442-y
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10182-022-00442-y
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10182-022-00442-y?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. Charles J. Corrado & Tie Su, 1996. "Skewness And Kurtosis In S&P 500 Index Returns Implied By Option Prices," Journal of Financial Research, Southern Finance Association;Southwestern Finance Association, vol. 19(2), pages 175-192, June.
    2. Jones, M. C. & Rosco, J. F. & Pewsey, Arthur, 2011. "Skewness-Invariant Measures of Kurtosis," The American Statistician, American Statistical Association, vol. 65(2), pages 89-95.
    3. Lucio Capitani & Leo Pasquazzi, 2015. "Inference for performance measures for financial assets," METRON, Springer;Sapienza Università di Roma, vol. 73(1), pages 73-98, April.
    4. Anna M. Fiori & Michele Zenga, 2009. "Karl Pearson and the Origin of Kurtosis," International Statistical Review, International Statistical Institute, vol. 77(1), pages 40-50, April.
    5. 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.
    6. Lionel Martellini & Volker Ziemann, 2010. "Improved Estimates of Higher-Order Comoments and Implications for Portfolio Selection," The Review of Financial Studies, Society for Financial Studies, vol. 23(4), pages 1467-1502, April.
    7. Charles J. Corrado & Tie Su, 1996. "Skewness And Kurtosis In S&P 500 Index Returns Implied By Option Prices," Journal of Financial Research, Southern Finance Association;Southwestern Finance Association, vol. 19(2), pages 175-192, June.
    8. Gastwirth, Joseph L, 1974. "Large Sample Theory of Some Measures of Income Inequality," Econometrica, Econometric Society, vol. 42(1), pages 191-196, January.
    9. M. Angeles Carnero, 2004. "Persistence and Kurtosis in GARCH and Stochastic Volatility Models," Journal of Financial Econometrics, Oxford University Press, vol. 2(2), pages 319-342.
    10. David C. Blest, 2003. "A New Measure of Kurtosis Adjusted for Skewness," Australian & New Zealand Journal of Statistics, Australian Statistical Publishing Association Inc., vol. 45(2), pages 175-179, June.
    Full references (including those not matched with items on IDEAS)

    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. Monica Billio & Bertrand Maillet & Loriana Pelizzon, 2022. "A meta-measure of performance related to both investors and investments characteristics," Annals of Operations Research, Springer, vol. 313(2), pages 1405-1447, June.
    2. Steven L. Heston & Alberto G. Rossi, 2017. "A Spanning Series Approach to Options," The Review of Asset Pricing Studies, Society for Financial Studies, vol. 7(1), pages 2-42.
    3. F. Cavalli & A. Naimzada & N. Pecora & M. Pireddu, 2021. "Market sentiment and heterogeneous agents in an evolutive financial model," Journal of Evolutionary Economics, Springer, vol. 31(4), pages 1189-1219, September.
    4. Ryszard Kokoszczyński & Paweł Sakowski & Robert Ślepaczuk, 2010. "Midquotes or Transactional Data? The Comparison of Black Model on HF Data," Working Papers 2010-15, Faculty of Economic Sciences, University of Warsaw.
    5. Topaloglou, Nikolas & Vladimirou, Hercules & Zenios, Stavros A., 2020. "Integrated dynamic models for hedging international portfolio risks," European Journal of Operational Research, Elsevier, vol. 285(1), pages 48-65.
    6. Pierre-Edouard Arrouy & Sophian Mehalla & Bernard Lapeyre & Alexandre Boumezoued, 2020. "Jacobi Stochastic Volatility factor for the Libor Market Model," Working Papers hal-02468583, HAL.
    7. Rompolis, Leonidas S., 2010. "Retrieving risk neutral densities from European option prices based on the principle of maximum entropy," Journal of Empirical Finance, Elsevier, vol. 17(5), pages 918-937, December.
    8. Pierre-Edouard Arrouy & Alexandre Boumezoued & Bernard Lapeyre & Sophian Mehalla, 2022. "Jacobi stochastic volatility factor for the LIBOR market model," Finance and Stochastics, Springer, vol. 26(4), pages 771-823, October.
    9. Gangadhar Nayak & Subhranshu Sekhar Tripathy & Agbotiname Lucky Imoize & Chun-Ta Li, 2024. "Application of Extended Normal Distribution in Option Price Sensitivities," Mathematics, MDPI, vol. 12(15), pages 1-18, July.
    10. Adamson, Seabron & Noe, Thomas & Parker, Geoffrey, 2010. "Efficiency of financial transmission rights markets in centrally coordinated periodic auctions," Energy Economics, Elsevier, vol. 32(4), pages 771-778, July.
    11. Richard Harris & C. Coskun Kucukozmen & Fatih Yilmaz, 2004. "Skewness in the conditional distribution of daily equity returns," Applied Financial Economics, Taylor & Francis Journals, vol. 14(3), pages 195-202.
    12. Gabriele Fiorentini & Angel León & Gonzalo Rubio, "undated". "Short-term options with stochastic volatility: Estimation and empirical performance," Studies on the Spanish Economy 02, FEDEA.
    13. Bodo Herzog & Sufyan Osamah, 2019. "Reverse Engineering of Option Pricing: An AI Application," IJFS, MDPI, vol. 7(4), pages 1-12, November.
    14. León, à ngel & Mencía, Javier & Sentana, Enrique, 2009. "Parametric Properties of Semi-Nonparametric Distributions, with Applications to Option Valuation," Journal of Business & Economic Statistics, American Statistical Association, vol. 27(2), pages 176-192.
    15. Johannes Ruf & Weiguan Wang, 2019. "Neural networks for option pricing and hedging: a literature review," Papers 1911.05620, arXiv.org, revised May 2020.
    16. Yuji Yamada & James Primbs, 2004. "Properties of Multinomial Lattices with Cumulants for Option Pricing and Hedging," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 11(3), pages 335-365, September.
    17. Vahamaa, Sami, 2005. "Option-implied asymmetries in bond market expectations around monetary policy actions of the ECB," Journal of Economics and Business, Elsevier, vol. 57(1), pages 23-38.
    18. Pal, Sumantra, 2018. "How to intervene in foreign exchange market without buying/selling dollars?," EconStor Preprints 181880, ZBW - Leibniz Information Centre for Economics.
    19. Marie Briere, 2006. "Market Reactions to Central Bank Communication Policies :Reading Interest Rate Options Smiles," Working Papers CEB 38, ULB -- Universite Libre de Bruxelles.
    20. Marie Brière & Kamal Chancari, 2004. "Perception des risques sur les marchés, construction d'un indice élaboré à partir des smiles d'options et test de stratégies," Revue d'économie politique, Dalloz, vol. 114(4), pages 527-555.

    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:spr:alstar:v:106:y:2022:i:4:d:10.1007_s10182-022-00442-y. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.