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A Test for the Portion of Bivariate Dependence in Multivariate Tail Risk

Author

Listed:
  • Carsten Bormann
  • Melanie Schienle

    (Leibniz Universität Hannover, Germany)

  • Julia Schaumburg

    (VU University Amsterdam)

Abstract

In practice, multivariate dependencies between extreme risks are often only assessed in a pairwise way. We propose a test to detect when tail dependence is truly high-dimensional and bivariate simplifications would produce misleading results. This occurs when a significant portion of the multivariate dependence structure in the tails is of higher dimension than two. Our test statistic is based on a decomposition of the stable tail dependence function, which is standard in extreme value theory for describing multivariate tail dependence. The asymptotic properties of the test are provided and a bootstrap based finite sample version of the test is suggested. A simulation study documents the good performance of the test for standard sample sizes. In an application to international government bonds, we detect a high tail{risk and low return situation during the last decade which can essentially be attributed to increased higher{order tail risk. We also illustrate the empirical consequences from ignoring higher-dimensional tail risk.

Suggested Citation

  • 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, revised 23 Jun 2014.
  • Handle: RePEc:tin:wpaper:20140024
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    References listed on IDEAS

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    1. P. Hartmann & S. Straetmans & C. G. de Vries, 2004. "Asset Market Linkages in Crisis Periods," The Review of Economics and Statistics, MIT Press, vol. 86(1), pages 313-326, February.
    2. Einmahl, J.H.J. & Krajina, A. & Segers, J., 2011. "An M-Estimator for Tail Dependence in Arbitrary Dimensions," Discussion Paper 2011-013, Tilburg University, Center for Economic Research.
    3. Geluk, J.L. & de Haan, L.F.M., 2002. "On bootstrap sample size in extreme value theory," Econometric Institute Research Papers EI 2002-40, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    4. Rosenberg, Joshua V. & Schuermann, Til, 2006. "A general approach to integrated risk management with skewed, fat-tailed risks," Journal of Financial Economics, Elsevier, vol. 79(3), pages 569-614, March.
    5. S. T. M. Straetmans & W. F. C. Verschoor & C. C. P. Wolff, 2008. "Extreme US stock market fluctuations in the wake of 9|11," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 23(1), pages 17-42.
    6. de Haan, Laurens & Neves, Cláudia & Peng, Liang, 2008. "Parametric tail copula estimation and model testing," Journal of Multivariate Analysis, Elsevier, vol. 99(6), pages 1260-1275, July.
    7. Einmahl, J.H.J. & de Haan, L.F.M. & Li, D., 2006. "Weighted approximations of tail copula processes with applications to testing the bivariate extreme value condition," Other publications TiSEM 18b65ac3-ba79-4bff-ad53-2, Tilburg University, School of Economics and Management.
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    More about this item

    Keywords

    decomposition of tail dependence; multivariate extreme values; stable tail dependence function; subsample bootstrap; tail correlation;

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C19 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Other

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