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Estimating the index of a stable distribution

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  • de Haan, L.
  • Pereira, T. Themido

Abstract

An estimator is proposed for the index a of a stable distribution (0 # [alpha] [less-than-or-equals, slant] 2) and the asymmetry parameter p (0 [less-than-or-equals, slant] p [less-than-or-equals, slant] 1) based on a sample from a probability distribution in the domain of attraction of the stable distribution.

Suggested Citation

  • de Haan, L. & Pereira, T. Themido, 1999. "Estimating the index of a stable distribution," Statistics & Probability Letters, Elsevier, vol. 41(1), pages 39-55, January.
    • Handle: RePEc:eee:stapro:v:41:y:1999:i:1:p:39-55
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    References listed on IDEAS

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    1. Csörgóo, Miklós & Horváth, Lajos, 1986. "Approximations of weighted empirical and quantile processes," Statistics & Probability Letters, Elsevier, vol. 4(6), pages 275-280, October.
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    Cited by:

    1. Danielsson, J. & de Haan, L. & Peng, L. & de Vries, C. G., 2001. "Using a Bootstrap Method to Choose the Sample Fraction in Tail Index Estimation," Journal of Multivariate Analysis, Elsevier, vol. 76(2), pages 226-248, February.
    2. Zhao, Zhibiao & Wu, Wei Biao, 2009. "Nonparametric inference of discretely sampled stable Lévy processes," Journal of Econometrics, Elsevier, vol. 153(1), pages 83-92, November.
    3. Igor Fedotenkov, 2020. "A Review of More than One Hundred Pareto-Tail Index Estimators," Statistica, Department of Statistics, University of Bologna, vol. 80(3), pages 245-299.
    4. Danielsson, Jon & Ergun, Lerby M. & Haan, Laurens de & Vries, Casper G. de, 2016. "Tail index estimation: quantile driven threshold selection," LSE Research Online Documents on Economics 66193, London School of Economics and Political Science, LSE Library.
    5. Benjamin R. Auer & Benjamin Mögel, 2016. "How Accurate are Modern Value-at-Risk Estimators Derived from Extreme Value Theory?," CESifo Working Paper Series 6288, CESifo.
    6. Ayoub Ammy-Driss & Matthieu Garcin, 2021. "Efficiency of the financial markets during the COVID-19 crisis: time-varying parameters of fractional stable dynamics," Working Papers hal-02903655, HAL.
    7. Ercan Balaban & Jamal Ouenniche & Danae Politou, 2005. "A note on return distribution of UK stock indices," Applied Economics Letters, Taylor & Francis Journals, vol. 12(9), pages 573-576.
    8. Ayoub Ammy-Driss & Matthieu Garcin, 2020. "Efficiency of the financial markets during the COVID-19 crisis: time-varying parameters of fractional stable dynamics," Papers 2007.10727, arXiv.org, revised Nov 2021.
    9. Laurens F.M. de Haan & Liang Peng & H. Iglesias Pereira, 1997. "Approximation by Penultimate Stable Laws," Tinbergen Institute Discussion Papers 97-100/4, Tinbergen Institute.
    10. Jaap Geluk & Liang Peng & Casper G. de Vries, 1999. "Convolutions of Heavy Tailed Random Variables and Applications to Portfolio Diversification and MA(1) Time Series," Tinbergen Institute Discussion Papers 99-088/2, Tinbergen Institute.
    11. Gaoge Hu & Shesheng Gao & Yongmin Zhong & Chengfan Gu, 2014. "Random weighting estimation of stable exponent," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 77(4), pages 451-468, May.
    12. Geluk, J. L. & Peng, Liang, 2000. "An adaptive optimal estimate of the tail index for MA(l) time series," Statistics & Probability Letters, Elsevier, vol. 46(3), pages 217-227, February.
    13. Allen, Michael R. & Datta, Somnath, 1999. "Estimation of the index parameter for autoregressive data using the estimated innovations," Statistics & Probability Letters, Elsevier, vol. 41(3), pages 315-324, February.
    14. Goddard, John & Onali, Enrico, 2012. "Self-affinity in financial asset returns," International Review of Financial Analysis, Elsevier, vol. 24(C), pages 1-11.
    15. Benjamin Mögel & Benjamin R. Auer, 2018. "How accurate are modern Value-at-Risk estimators derived from extreme value theory?," Review of Quantitative Finance and Accounting, Springer, vol. 50(4), pages 979-1030, May.
    16. Ma, Yaolan & Jiang, Yuexiang & Huang, Wei, 2018. "Empirical likelihood based inference for conditional Pareto-type tail index," Statistics & Probability Letters, Elsevier, vol. 134(C), pages 114-121.
    17. Ammy-Driss, Ayoub & Garcin, Matthieu, 2023. "Efficiency of the financial markets during the COVID-19 crisis: Time-varying parameters of fractional stable dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 609(C).
    18. Groenendijk, Patrick A. & Lucas, Andre & de Vries, Casper G., 1995. "A note on the relationship between GARCH and symmetric stable processes," Journal of Empirical Finance, Elsevier, vol. 2(3), pages 253-264, September.
    19. Brito, Margarida & Moreira Freitas, Ana Cristina, 2003. "Limiting behaviour of a geometric-type estimator for tail indices," Insurance: Mathematics and Economics, Elsevier, vol. 33(2), pages 211-226, October.
    20. Osman Doğan & Süleyman Taşpınar & Anil K. Bera, 2021. "Bayesian estimation of stochastic tail index from high-frequency financial data," Empirical Economics, Springer, vol. 61(5), pages 2685-2711, November.

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