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Statistics of Heteroscedastic Extremes

Author

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  • Einmahl, J.H.J.

    (Tilburg University, Center For Economic Research)

  • 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," Discussion Paper 2014-015, Tilburg University, Center for Economic Research.
    • Handle: RePEc:tiu:tiucen: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," Other publications TiSEM dd3c4dd0-7181-40f3-af44-f, Tilburg University, School of Economics and Management.
    2. Jacek Wójcik, 2017. "Consequences of the Cognitive Digital Divide on the Consumer Market," Collegium of Economic Analysis Annals, Warsaw School of Economics, Collegium of Economic Analysis, issue 44, pages 69-80.
    3. Einmahl, John & Ferreira, Ana & de Haan, Laurens & Neves, C. & Zhou, C., 2020. "Spatial Dependence and Space-Time Trend in Extreme Events," Other publications TiSEM ae5818cd-f071-4275-9577-d, Tilburg University, School of Economics and Management.
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    10. Einmahl, John & He, Y., 2020. "Unified Extreme Value Estimation for Heterogeneous Data," Discussion Paper 2020-025, Tilburg University, Center for Economic Research.
    11. Joos, Michael & Staffell, Iain, 2018. "Short-term integration costs of variable renewable energy: Wind curtailment and balancing in Britain and Germany," Renewable and Sustainable Energy Reviews, Elsevier, vol. 86(C), pages 45-65.
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    13. 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.
    14. Yaolan Ma & Bo Wei & Wei Huang, 2020. "A nonparametric estimator for the conditional tail index of Pareto-type distributions," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 83(1), pages 17-44, January.
    15. Li, Wei & Lu, Can & Ding, Yi & Zhang, Yan-Wu, 2017. "The impacts of policy mix for resolving overcapacity in heavy chemical industry and operating national carbon emission trading market in China," Applied Energy, Elsevier, vol. 204(C), pages 509-524.
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    18. Ljungberg, Anders, 2016. "Marginal cost-pricing in the Swedish transport sector – An efficient and sustainable way of funding local and regional public transport in the future?," Research in Transportation Economics, Elsevier, vol. 59(C), pages 159-166.
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    22. Everard, Mark & Longhurst, James & Pontin, John & Stephenson, Wendy & Brooks, Joss, 2017. "Developed-developing world partnerships for sustainable development (2): An illustrative case for a payments for ecosystem services (PES) approach," Ecosystem Services, Elsevier, vol. 24(C), pages 253-260.

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