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

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  • Carsten Bormann
  • Melanie Schienle
  • Julia Schaumburg

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 simpli cations would produce misleading results. This occurs when a signi cant 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 nite 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. "Beyond dimension two: A test for higher-order tail risk," SFB 649 Discussion Papers SFB649DP2014-042, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  • Handle: RePEc:hum:wpaper:sfb649dp2014-042
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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:

    • 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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