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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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    More about this item

    Keywords

    decomposition of tail dependence; multivariate extreme values; stable tail dependence function; subsample bootstrap; tail correlation;
    All these keywords.

    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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