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

  • Bonato, Matteo
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    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.

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    Article provided by Elsevier in its journal Finance Research Letters.

    Volume (Year): 8 (2011)
    Issue (Month): 2 (June)
    Pages: 77-87

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    Handle: RePEc:eee:finlet:v:8:y:2011:i:2:p:77-87
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    1. 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.
    2. 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.
    3. 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.
    4. Benoit Mandelbrot, 1963. "The Variation of Certain Speculative Prices," The Journal of Business, University of Chicago Press, vol. 36, pages 394.
    5. Campbell R. Harvey & Akhtar Siddique, 2000. "Conditional Skewness in Asset Pricing Tests," Journal of Finance, American Finance Association, vol. 55(3), pages 1263-1295, 06.
    6. 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.
    7. Stephen Satchell & Soosung Hwang, 1999. "Modelling Emerging Market Risk Premia Using Higher Moments," Working Papers wp99-17, Warwick Business School, Finance Group.
    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. 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.
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