IDEAS home Printed from https://ideas.repec.org/a/eee/finlet/v8y2011i2p77-87.html
   My bibliography  Save this article

Robust estimation of skewness and kurtosis in distributions with infinite higher moments

Author

Listed:
  • Bonato, Matteo

Abstract

This paper studies the behavior of the conventional measures of skewness and kurtosis when the data generator process is a distribution which does not possess variance or third or fourth moment and assesses the robustness of the alternative measures for these particular cases. It is first shown that for symmetric fat-tailed distribution skewness is far from being a valid indicator of the presence of asymmetry. Secondly, a Monte Carlo simulation is performed to investigate the behavior of the alternative measures of skewness and kurtosis when applied to distributions which do not possess finite higher moments. Finally, an application to the series of daily returns on a large cap US stock is presented to explain why alternative measures are a better tool to describe the distribution of financial returns.

Suggested Citation

  • Bonato, Matteo, 2011. "Robust estimation of skewness and kurtosis in distributions with infinite higher moments," Finance Research Letters, Elsevier, vol. 8(2), pages 77-87, June.
  • Handle: RePEc:eee:finlet:v:8:y:2011:i:2:p:77-87
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S154461231000067X
    Download Restriction: Full text for ScienceDirect subscribers only

    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. Hwang, Soosung & Satchell, Stephen E, 1999. "Modelling Emerging Market Risk Premia Using Higher Moments," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 4(4), pages 271-296, October.
    2. Ding, Zhuanxin & Granger, Clive W. J. & Engle, Robert F., 1993. "A long memory property of stock market returns and a new model," Journal of Empirical Finance, Elsevier, vol. 1(1), pages 83-106, June.
    3. Harvey, Campbell R. & Siddique, Akhtar, 1999. "Autoregressive Conditional Skewness," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 34(04), pages 465-487, December.
    4. Benoit Mandelbrot, 2015. "The Variation of Certain Speculative Prices," World Scientific Book Chapters,in: THE WORLD SCIENTIFIC HANDBOOK OF FUTURES MARKETS, chapter 3, pages 39-78 World Scientific Publishing Co. Pte. Ltd..
    5. Kim, Tae-Hwan & White, Halbert, 2004. "On more robust estimation of skewness and kurtosis," Finance Research Letters, Elsevier, vol. 1(1), pages 56-73, March.
    6. Bates, David S, 1996. "Jumps and Stochastic Volatility: Exchange Rate Processes Implicit in Deutsche Mark Options," Review of Financial Studies, Society for Financial Studies, vol. 9(1), pages 69-107.
    7. Campbell R. Harvey & Akhtar Siddique, 2000. "Conditional Skewness in Asset Pricing Tests," Journal of Finance, American Finance Association, vol. 55(3), pages 1263-1295, June.
    8. Philippe Jorion, 1988. "On Jump Processes in the Foreign Exchange and Stock Markets," Review of Financial Studies, Society for Financial Studies, vol. 1(4), pages 427-445.
    9. Mittnik, Stefan & Paolella, Marc S. & Rachev, Svetlozar T., 2000. "Diagnosing and treating the fat tails in financial returns data," Journal of Empirical Finance, Elsevier, vol. 7(3-4), pages 389-416, November.
    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. repec:eee:energy:v:138:y:2017:i:c:p:967-976 is not listed on IDEAS
    2. Matteo Bonato, 2012. "Modeling fat tails in stock returns: a multivariate stable-GARCH approach," Computational Statistics, Springer, vol. 27(3), pages 499-521, September.
    3. Kim, Yunmi & Kim, Tae-Hwan & Erg√ľn, Tolga, 2015. "The instability of the Pearson correlation coefficient in the presence of coincidental outliers," Finance Research Letters, Elsevier, vol. 13(C), pages 243-257.
    4. Huo, Lijuan & Kim, Tae-Hwan & Kim, Yunmi, 2012. "Robust estimation of covariance and its application to portfolio optimization," Finance Research Letters, Elsevier, vol. 9(3), pages 121-134.

    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:finlet:v:8:y:2011:i:2:p:77-87. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Dana Niculescu). General contact details of provider: http://www.elsevier.com/locate/frl .

    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 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.

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.