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Non-parametric Estimation of Tail Dependence

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  • RAFAEL SCHMIDT
  • ULRICH STADTMÜLLER
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    Abstract

    Dependencies between extreme events (extremal dependencies) are attracting an increasing attention in modern risk management. In practice, the concept of tail dependence represents the current standard to describe the amount of extremal dependence. In theory, multi-variate extreme-value theory turns out to be the natural choice to model the latter dependencies. The present paper embeds tail dependence into the concept of tail copulae which describes the dependence structure in the tail of multivariate distributions but works more generally. Various non-parametric estimators for tail copulae and tail dependence are discussed, and weak convergence, asymptotic normality, and strong consistency of these estimators are shown by means of a functional delta method. Further, weak convergence of a general upper-order rank-statistics for extreme events is investigated and the relationship to tail dependence is provided. A simulation study compares the introduced estimators and two financial data sets were analysed by our methods. Copyright 2006 Board of the Foundation of the Scandinavian Journal of Statistics..

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    File URL: http://www.blackwell-synergy.com/doi/abs/10.1111/j.1467-9469.2005.00483.x
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    Bibliographic Info

    Article provided by Danish Society for Theoretical Statistics & Finnish Statistical Society & Norwegian Statistical Association & Swedish Statistical Association in its journal Scandinavian Journal of Statistics.

    Volume (Year): 33 (2006)
    Issue (Month): 2 ()
    Pages: 307-335

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    Handle: RePEc:bla:scjsta:v:33:y:2006:i:2:p:307-335

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    Cited by:
    1. Ferreira, Helena & Ferreira, Marta, 2012. "Tail dependence between order statistics," Journal of Multivariate Analysis, Elsevier, vol. 105(1), pages 176-192.
    2. Li, Deyuan & Peng, Liang, 2009. "Goodness-of-fit test for tail copulas modeled by elliptical copulas," Statistics & Probability Letters, Elsevier, vol. 79(8), pages 1097-1104, April.
    3. Choroś-Tomczyk, Barbara & Härdle, Wolfgang Karl & Okhrin, Ostap, 2013. "Valuation of collateralized debt obligations with hierarchical Archimedean copulae," Journal of Empirical Finance, Elsevier, vol. 24(C), pages 42-62.
    4. Fischer, Matthias J. & Dörflinger, Marco, 2006. "A note on a non-parametric tail dependence estimator," Discussion Papers 76/2006, Friedrich-Alexander-University Erlangen-Nuremberg, Chair of Statistics and Econometrics.
    5. Hua, Lei & Joe, Harry, 2014. "Strength of tail dependence based on conditional tail expectation," Journal of Multivariate Analysis, Elsevier, vol. 123(C), pages 143-159.
    6. Marta Ferreira & Helena Ferreira, 2013. "Extremes of multivariate ARMAX processes," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer, vol. 22(4), pages 606-627, November.
    7. Weiß, Gregor N.F. & Bostandzic, Denefa & Neumann, Sascha, 2014. "What factors drive systemic risk during international financial crises?," Journal of Banking & Finance, Elsevier, vol. 41(C), pages 78-96.
    8. Carsten Bormann & Melanie Schienle & Julia Schaumburg, 2014. "A Test for the Portion of Bivariate Dependence in Multivariate Tail Risk," Tinbergen Institute Discussion Papers 14-024/III, Tinbergen Institute.
    9. Nikoloulopoulos, Aristidis K. & Joe, Harry & Li, Haijun, 2012. "Vine copulas with asymmetric tail dependence and applications to financial return data," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3659-3673.
    10. Herrera, R. & Eichler, S., 2011. "Extreme dependence with asymmetric thresholds: Evidence for the European Monetary Union," Journal of Banking & Finance, Elsevier, vol. 35(11), pages 2916-2930, November.
    11. Georg Mainik & Ludger Rüschendorf, 2010. "On optimal portfolio diversification with respect to extreme risks," Finance and Stochastics, Springer, vol. 14(4), pages 593-623, December.
    12. Wu, Ximing, 2010. "Exponential Series Estimator of multivariate densities," Journal of Econometrics, Elsevier, vol. 156(2), pages 354-366, June.
    13. Marta Ferreira & Helena Ferreira, 2012. "On extremal dependence: some contributions," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer, vol. 21(3), pages 566-583, September.
    14. Weiß, Gregor N.F. & Neumann, Sascha & Bostandzic, Denefa, 2014. "Systemic risk and bank consolidation: International evidence," Journal of Banking & Finance, Elsevier, vol. 40(C), pages 165-181.
    15. Weiß, Gregor N.F. & Supper, Hendrik, 2013. "Forecasting liquidity-adjusted intraday Value-at-Risk with vine copulas," Journal of Banking & Finance, Elsevier, vol. 37(9), pages 3334-3350.
    16. Zhang, Qingzhao & Li, Deyuan & Wang, Hansheng, 2013. "A note on tail dependence regression," Journal of Multivariate Analysis, Elsevier, vol. 120(C), pages 163-172.
    17. Münnix, Michael C. & Schäfer, Rudi, 2011. "A copula approach on the dynamics of statistical dependencies in the US stock market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(23), pages 4251-4259.
    18. Ranoua Bouchouicha, 2010. "Dépendance entre risques extrêmes : Application aux Hedge Funds," Working Papers 1013, Groupe d'Analyse et de Théorie Economique (GATE), Centre national de la recherche scientifique (CNRS), Université Lyon 2, Ecole Normale Supérieure.

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