IDEAS home Printed from https://ideas.repec.org/p/hal/journl/hal-02311834.html
   My bibliography  Save this paper

On the Power of Generalized Extreme Value (GEV) and Generalized Pareto Distribution (GPD) Estimators for Empirical Distributions of Stock Returns

Author

Listed:
  • Yannick Malevergne

    (EM - EMLyon Business School)

  • Vladilen Pisarenko
  • Didier Sornette

Abstract

Using synthetic tests performed on time series with time dependence in the volatility with both Pareto and Stretched-Exponential distributions, it is shown that for samples of moderate sizes the standard generalized extreme value (GEV) estimator is quite inefficient due to the possibly slow convergence toward the asymptotic theoretical distribution and the existence of biases in the presence of dependence between data. Thus, it cannot distinguish reliably between rapidly and regularly varying classes of distributions. The Generalized Pareto distribution (GPD) estimator works better, but still lacks power in the presence of strong dependence. Applied to 100 years of daily returns of the Dow Jones Industrial Average and over one years of five-minutes returns of the Nasdaq Composite index, the GEV and GDP estimators are found insufficient to prove that the distributions of empirical returns of financial time series are regularly varying, because the rapidly varying exponential or stretched exponential distributions are equally acceptable.

Suggested Citation

  • Yannick Malevergne & Vladilen Pisarenko & Didier Sornette, 2006. "On the Power of Generalized Extreme Value (GEV) and Generalized Pareto Distribution (GPD) Estimators for Empirical Distributions of Stock Returns," Post-Print hal-02311834, HAL.
    • Handle: RePEc:hal:journl:hal-02311834
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a search for a similarly titled item that would be available.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Yannick Malevergne & Didier Sornette, 2006. "Extreme Financial Risks : From Dependence to Risk Management," Post-Print hal-02298069, HAL.
    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. Jose Fernandes & Augusto Hasman & Juan Ignacio Pena, 2007. "Risk premium: insights over the threshold," Applied Financial Economics, Taylor & Francis Journals, vol. 18(1), pages 41-59.
    2. Marcin Wk{a}torek & Jaros{l}aw Kwapie'n & Stanis{l}aw Dro.zd.z, 2021. "Financial Return Distributions: Past, Present, and COVID-19," Papers 2107.06659, arXiv.org.
    3. Li, Wei-Zhen & Zhai, Jin-Rui & Jiang, Zhi-Qiang & Wang, Gang-Jin & Zhou, Wei-Xing, 2022. "Predicting tail events in a RIA-EVT-Copula framework," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 600(C).
    4. Gu, Gao-Feng & Chen, Wei & Zhou, Wei-Xing, 2008. "Empirical distributions of Chinese stock returns at different microscopic timescales," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(2), pages 495-502.
    5. Bonga-Bonga, Lumengo & Montshioa, Keitumetse, 2024. "Navigating extreme market fluctuations: asset allocation strategies in developed vs. emerging economies," MPRA Paper 119910, University Library of Munich, Germany.
    6. Salhi, Khaled & Deaconu, Madalina & Lejay, Antoine & Champagnat, Nicolas & Navet, Nicolas, 2016. "Regime switching model for financial data: Empirical risk analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 461(C), pages 148-157.
    7. Bertrand B. Maillet & Jean-Philippe R. M�decin, 2010. "Extreme Volatilities, Financial Crises and L-moment Estimations of Tail-indexes," Working Papers 2010_10, Department of Economics, University of Venice "Ca' Foscari".
    8. Rakhee Dinubhai Patel & Frederic Paik Schoenberg, 2011. "A graphical test for local self-similarity in univariate data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(11), pages 2547-2562, January.
    9. George Haiman, 2018. "Level Hitting Probabilities and Extremal Indexes for Some Particular Dynamical Systems," Methodology and Computing in Applied Probability, Springer, vol. 20(2), pages 553-562, June.
    10. V. F. Pisarenko & D. Sornette, 2004. "New statistic for financial return distributions: power-law or exponential?," Papers physics/0403075, arXiv.org.
    11. Matteo Gentilucci & Alessandro Rossi & Niccolò Pelagagge & Domenico Aringoli & Maurizio Barbieri & Gilberto Pambianchi, 2023. "GEV Analysis of Extreme Rainfall: Comparing Different Time Intervals to Analyse Model Response in Terms of Return Levels in the Study Area of Central Italy," Sustainability, MDPI, vol. 15(15), pages 1-25, July.
    12. Montshioa, Keitumetse & Muteba Mwamba, John Weirstrass & Bonga-Bonga, Lumengo, 2021. "Asset allocation in extreme market conditions: a comparative analysis between developed and emerging economies," MPRA Paper 106248, University Library of Munich, Germany.

    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. Alves, L.G.A. & Ribeiro, H.V. & Lenzi, E.K. & Mendes, R.S., 2014. "Empirical analysis on the connection between power-law distributions and allometries for urban indicators," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 409(C), pages 175-182.
    2. Donatien Hainaut & Renaud MacGilchrist, 2012. "Strategic asset allocation with switching dependence," Annals of Finance, Springer, vol. 8(1), pages 75-96, February.
    3. Diana, Tony, 2011. "Improving schedule reliability based on copulas: An application to five of the most congested US airports," Journal of Air Transport Management, Elsevier, vol. 17(5), pages 284-287.
    4. Dietmar Pfeifer & Olena Ragulina, 2018. "Generating VaR Scenarios under Solvency II with Product Beta Distributions," Risks, MDPI, vol. 6(4), pages 1-15, October.
    5. Hernández-Ramírez, E. & del Castillo-Mussot, M. & Hernández-Casildo, J., 2021. "World per capita gross domestic product measured nominally and across countries with purchasing power parity: Stretched exponential or Boltzmann–Gibbs distribution?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 568(C).
    6. Tang, Qihe & Yang, Fan, 2012. "On the Haezendonck–Goovaerts risk measure for extreme risks," Insurance: Mathematics and Economics, Elsevier, vol. 50(1), pages 217-227.
    7. César Garcia-Gomez & Ana Pérez & Mercedes Prieto-Alaiz, 2022. "The evolution of poverty in the EU-28: a further look based on multivariate tail dependence," Working Papers 605, ECINEQ, Society for the Study of Economic Inequality.
    8. Sornette, Didier & Zhou, Wei-Xing, 2006. "Importance of positive feedbacks and overconfidence in a self-fulfilling Ising model of financial markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 370(2), pages 704-726.
    9. M. Wili'nski & A. Sienkiewicz & T. Gubiec & R. Kutner & Z. R. Struzik, 2013. "Structural and topological phase transitions on the German Stock Exchange," Papers 1301.2530, arXiv.org, revised Jul 2013.
    10. Sandro Claudio Lera & Didier Sornette, 2015. "Currency target zone modeling: An interplay between physics and economics," Papers 1508.04754, arXiv.org, revised Oct 2015.
    11. Fantazzini, Dean, 2011. "Analysis of multidimensional probability distributions with copula functions," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 22(2), pages 98-134.
    12. Mateusz Denys & Maciej Jagielski & Tomasz Gubiec & Ryszard Kutner & H. Eugene Stanley, 2015. "Universality of market superstatistics," Papers 1509.06315, arXiv.org.
    13. Chen, Wang & Wei, Yu & Lang, Qiaoqi & Lin, Yu & Liu, Maojuan, 2014. "Financial market volatility and contagion effect: A copula–multifractal volatility approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 398(C), pages 289-300.
    14. Martin Eling & Simone Farinelli & Damiano Rossello & Luisa Tibiletti, 2010. "Skewness in hedge funds returns: classical skewness coefficients vs Azzalini's skewness parameter," International Journal of Managerial Finance, Emerald Group Publishing Limited, vol. 6(4), pages 290-304, September.
    15. Christian Genest & Michel Gendron & Michaël Bourdeau-Brien, 2009. "The Advent of Copulas in Finance," The European Journal of Finance, Taylor & Francis Journals, vol. 15(7-8), pages 609-618.
    16. Zhou, Wei-Xing, 2012. "Finite-size effect and the components of multifractality in financial volatility," Chaos, Solitons & Fractals, Elsevier, vol. 45(2), pages 147-155.
    17. Wei-han Liu, 2013. "Detecting structural breaks in tail behaviour -- from the perspective of fitting the generalized Pareto distribution," Applied Economics, Taylor & Francis Journals, vol. 45(10), pages 1273-1286, April.
    18. Alexander Saichev & Thomas Maillart & Didier Sornette, 2013. "Hierarchy of temporal responses of multivariate self-excited epidemic processes," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 86(4), pages 1-19, April.
    19. A. Sienkiewicz & T. Gubiec & R. Kutner & Z. R. Struzik, 2013. "Dynamic structural and topological phase transitions on the Warsaw Stock Exchange: A phenomenological approach," Papers 1301.6506, arXiv.org.
    20. John Fry & McMillan David, 2015. "Stochastic modelling for financial bubbles and policy," Cogent Economics & Finance, Taylor & Francis Journals, vol. 3(1), pages 1002152-100, December.

    More about this item

    Statistics

    Access and download statistics

    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:hal:journl:hal-02311834. 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: CCSD (email available below). General contact details of provider: https://hal.archives-ouvertes.fr/ .

    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.