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Statistics of heteroscedastic extremes

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  • John H. J. Einmahl
  • Laurens Haan
  • Chen Zhou

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

  • John H. J. Einmahl & Laurens Haan & Chen Zhou, 2016. "Statistics of heteroscedastic extremes," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 78(1), pages 31-51, January.
  • Handle: RePEc:bla:jorssb:v:78:y:2016:i:1:p:31-51
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    1. 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.
    2. Einmahl, J.H.J. & Gantner, M. & Sawitzki, G., 2008. "The Shorth Plot," Discussion Paper 2008-24, Tilburg University, Center for Economic Research.
    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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    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. 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.
    3. 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.
    4. 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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    14. Dominković, D.F. & Bačeković, I. & Ćosić, B. & Krajačić, G. & Pukšec, T. & Duić, N. & Markovska, N., 2016. "Zero carbon energy system of South East Europe in 2050," Applied Energy, Elsevier, vol. 184(C), pages 1517-1528.
    15. Demichelis, Francesca & Fiore, Silvia & Pleissner, Daniel & Venus, Joachim, 2018. "Technical and economic assessment of food waste valorization through a biorefinery chain," Renewable and Sustainable Energy Reviews, Elsevier, vol. 94(C), pages 38-48.
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    18. Schweiger, Gerald & Rantzer, Jonatan & Ericsson, Karin & Lauenburg, Patrick, 2017. "The potential of power-to-heat in Swedish district heating systems," Energy, Elsevier, vol. 137(C), pages 661-669.
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    21. Einmahl, John & He, Y., 2020. "Unified Extreme Value Estimation for Heterogeneous Data," Discussion Paper 2020-025, Tilburg University, Center for Economic Research.
    22. 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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