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Statistics of Heteroscedastic Extremes

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  • Einmahl, J.H.J.

    (Tilburg University, School of Economics and Management)

  • de Haan, L.F.M.
  • Zhou, C.

Abstract

Abstract: We extend classical extreme value theory to non-identically distributed observations. When the distribution tails are proportional much of extreme value statistics remains valid. The proportionality function for the tails can be estimated nonparametrically along with the (common) extreme value index. Joint asymptotic normality of both estimators is shown; they are asymptotically independent. We develop tests for the proportionality function and for the validity of the model. We show through simulations the good performance of tests for tail homoscedasticity. The results are applied to stock market returns. A main tool is the weak convergence of a weighted sequential tail empirical process.
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Suggested Citation

  • Einmahl, J.H.J. & de Haan, L.F.M. & Zhou, C., 2014. "Statistics of Heteroscedastic Extremes," Other publications TiSEM 19952ae4-25ff-4e1b-8627-d, Tilburg University, School of Economics and Management.
  • Handle: RePEc:tiu:tiutis:19952ae4-25ff-4e1b-8627-d21d7a62375b
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    References listed on IDEAS

    as
    1. Einmahl, J.H.J. & Gantner, M. & Sawitzki, G., 2008. "The Shorth Plot," Discussion Paper 2008-24, Tilburg University, Center for Economic Research.
    2. Jansen, Dennis W & de Vries, Casper G, 1991. "On the Frequency of Large Stock Returns: Putting Booms and Busts into Perspective," The Review of Economics and Statistics, MIT Press, vol. 73(1), pages 18-24, February.
    3. Carmela Quintos & Zhenhong Fan & Peter C. B. Phillips, 2001. "Structural Change Tests in Tail Behaviour and the Asian Crisis," Review of Economic Studies, Oxford University Press, vol. 68(3), pages 633-663.
    4. Phillip Kearns & Adrian Pagan, 1997. "Estimating The Density Tail Index For Financial Time Series," The Review of Economics and Statistics, MIT Press, vol. 79(2), pages 171-175, May.
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    Cited by:

    1. Einmahl, John & Yang, Fan & Zhou, Chen, 2018. "Testing the Multivariate Regular Variation Model," Discussion Paper 2018-044, Tilburg University, Center for Economic Research.
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    6. Einmahl, John & He, Y., 2020. "Unified Extreme Value Estimation for Heterogeneous Data," Discussion Paper 2020-025, Tilburg University, Center for Economic Research.
    7. Einmahl, John & He, Y., 2020. "Unified Extreme Value Estimation for Heterogeneous Data," Other publications TiSEM dfe6c38c-823b-4394-b4fd-a, Tilburg University, School of Economics and Management.
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