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On the power of generalized extreme value (GEV) and generalized Pareto distribution (GPD) estimators for empirical distributions of stock returns

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  • Y. Malevergne
  • V. Pisarenko
  • D. 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

  • Y. Malevergne & V. Pisarenko & D. Sornette, 2006. "On the power of generalized extreme value (GEV) and generalized Pareto distribution (GPD) estimators for empirical distributions of stock returns," Applied Financial Economics, Taylor & Francis Journals, vol. 16(3), pages 271-289.
    • Handle: RePEc:taf:apfiec:v:16:y:2006:i:3:p:271-289
    DOI: 10.1080/09603100500391008
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    References listed on IDEAS

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    1. Yannick Malevergne & Didier Sornette, 2006. "Extreme Financial Risks : From Dependence to Risk Management," Post-Print hal-02298069, HAL.
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    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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".
    7. 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.
    8. 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.
    9. 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).
    10. 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.
    11. 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.
    12. V. F. Pisarenko & D. Sornette, 2004. "New statistic for financial return distributions: power-law or exponential?," Papers physics/0403075, arXiv.org.

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