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Monte Carlo-Based Tail Exponent Estimator



In this paper we study the finite sample behavior of the Hill estimator under α-stable distributions. Using large Monte Carlo simulations we show that the Hill estimator overestimates the true tail exponent and can hardly be used on samples with small length. Utilizing our results, we introduce a Monte Carlo-based method of estimation for the tail exponent. Our method is not sensitive to the choice of k and works well also on small samples. The new estimator gives unbiased results with symmetrical con_dence intervals. Finally, we demonstrate the power of our estimator on the main world stock market indices. On the two separate periods of 2002-2005 and 2006-2009 we estimate the tail exponent.

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  • Jozef Barunik & Lukas Vacha, 2010. "Monte Carlo-Based Tail Exponent Estimator," Working Papers IES 2010/06, Charles University Prague, Faculty of Social Sciences, Institute of Economic Studies, revised Apr 2010.
  • Handle: RePEc:fau:wpaper:wp2010_06

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    References listed on IDEAS

    1. Plerou, V & Gopikrishnan, P & Rosenow, B & Amaral, L.A.N & Stanley, H.E, 2000. "A random matrix theory approach to financial cross-correlations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 287(3), pages 374-382.
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    3. Szymon Borak & Wolfgang Härdle & Rafal Weron, 2005. "Stable Distributions," SFB 649 Discussion Papers SFB649DP2005-008, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    4. Xavier Gabaix & Rustam Ibragimov, 2011. "Rank - 1 / 2: A Simple Way to Improve the OLS Estimation of Tail Exponents," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 29(1), pages 24-39, January.
    5. Rafał Weron, 2001. "Levy-Stable Distributions Revisited: Tail Index> 2does Not Exclude The Levy-Stable Regime," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 12(02), pages 209-223.
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    Cited by:

    1. Barunik, Jozef & Aste, Tomaso & Di Matteo, T. & Liu, Ruipeng, 2012. "Understanding the source of multifractality in financial markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(17), pages 4234-4251.

    More about this item


    Hill estimator; α-stable distributions; tail exponent estimation;

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • G0 - Financial Economics - - General

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