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Beyond dimension two: A test for higher-order tail risk

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  • Bormann, Carsten
  • Schaumburg, Julia
  • Schienle, Melanie

Abstract

In practice, multivariate dependencies between extreme risks are often only assessed in a pairwise way. We propose a test for detecting situations when such pairwise measures are inadequate and give incomplete 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 describing multivariate tail dependence. The asymptotic properties of the test are provided and a bootstrap based finite sample version of the test is proposed. A simulation study documents good size and power properties of the test including settings with time-series components and factor models. In an application to stock indices for non-crisis times, pairwise tail models seem appropriate for global markets while the test finds them not admissible for the tightly interconnected European market. From 2007/08 on, however, higher order dependencies generally increase and require a multivariate tail model in all cases.

Suggested Citation

  • Bormann, Carsten & Schaumburg, Julia & Schienle, Melanie, 2016. "Beyond dimension two: A test for higher-order tail risk," Working Paper Series in Economics 80, Karlsruhe Institute of Technology (KIT), Department of Economics and Business Engineering.
  • Handle: RePEc:zbw:kitwps:80
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    References listed on IDEAS

    as
    1. P. Hartmann & S. Straetmans & C.G. de Vries, 2001. "Asset Market Linkages in Crisis Periods," Tinbergen Institute Discussion Papers 01-071/2, Tinbergen Institute.
    2. 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.
    3. Einmahl, J.H.J. & Krajina, A. & Segers, J.J.J., 2007. "A Method of Moments Estimator of Tail Dependence," Discussion Paper 2007-80, Tilburg University, Center for Economic Research.
    4. McNeil, Alexander J. & Frey, Rudiger, 2000. "Estimation of tail-related risk measures for heteroscedastic financial time series: an extreme value approach," Journal of Empirical Finance, Elsevier, pages 271-300.
    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. 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.
    7. Peter Christoffersen & Vihang Errunza & Kris Jacobs & Hugues Langlois, 2012. "Is the Potential for International Diversification Disappearing? A Dynamic Copula Approach," Review of Financial Studies, Society for Financial Studies, pages 3711-3751.
    8. 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.
    9. Ang, Andrew & Chen, Joseph, 2002. "Asymmetric correlations of equity portfolios," Journal of Financial Economics, Elsevier, vol. 63(3), pages 443-494, March.
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    More about this item

    Keywords

    decomposition of multivariate tail dependence; multivariate extreme values; stable tail dependence function; extreme dependence modeling;

    JEL classification:

    • C01 - Mathematical and Quantitative Methods - - General - - - Econometrics
    • C46 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Specific Distributions
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics

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