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Extreme Value Analysis for Mixture Models with Heavy-Tailed Impurity

Author

Listed:
  • Ekaterina Morozova

    (Laboratory of Stochastic Analysis and Its Applications, HSE University, Pokrovsky Boulevard 11, 109028 Moscow, Russia)

  • Vladimir Panov

    (Laboratory of Stochastic Analysis and Its Applications, HSE University, Pokrovsky Boulevard 11, 109028 Moscow, Russia)

Abstract

This paper deals with the extreme value analysis for the triangular arrays which appear when some parameters of the mixture model vary as the number of observations grows. When the mixing parameter is small, it is natural to associate one of the components with “an impurity” (in the case of regularly varying distribution, “heavy-tailed impurity”), which “pollutes” another component. We show that the set of possible limit distributions is much more diverse than in the classical Fisher–Tippett–Gnedenko theorem, and provide the numerical examples showing the efficiency of the proposed model for studying the maximal values of the stock returns.

Suggested Citation

  • Ekaterina Morozova & Vladimir Panov, 2021. "Extreme Value Analysis for Mixture Models with Heavy-Tailed Impurity," Mathematics, MDPI, vol. 9(18), pages 1-24, September.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:18:p:2208-:d:631951
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    References listed on IDEAS

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    1. Aban, Inmaculada B. & Meerschaert, Mark M. & Panorska, Anna K., 2006. "Parameter Estimation for the Truncated Pareto Distribution," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 270-277, March.
    2. Panov, Vladimir, 2017. "Limit theorems for sums of random variables with mixture distribution," Statistics & Probability Letters, Elsevier, vol. 129(C), pages 379-386.
    3. Y. Malevergne & V. Pisarenko & D. Sornette, 2005. "Empirical distributions of stock returns: between the stretched exponential and the power law?," Quantitative Finance, Taylor & Francis Journals, vol. 5(4), pages 379-401.
    4. R. Cont, 2001. "Empirical properties of asset returns: stylized facts and statistical issues," Quantitative Finance, Taylor & Francis Journals, vol. 1(2), pages 223-236.
    5. Benoit Mandelbrot, 2015. "The Variation of Certain Speculative Prices," World Scientific Book Chapters, in: Anastasios G Malliaris & William T Ziemba (ed.), THE WORLD SCIENTIFIC HANDBOOK OF FUTURES MARKETS, chapter 3, pages 39-78, World Scientific Publishing Co. Pte. Ltd..
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