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

Carsten Bormann, Melanie Schienle and Julia Schaumburg
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Melanie Schienle: Leibniz Universität Hannover, Germany

No 14-024/III, Tinbergen Institute Discussion Papers from Tinbergen Institute

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.

Keywords: decomposition of tail dependence; multivariate extreme values; stable tail dependence function; subsample bootstrap; tail correlation (search for similar items in EconPapers)
JEL-codes: C12 C19 (search for similar items in EconPapers)
Date: 2014-02-25, Revised 2014-06-23
New Economics Papers: this item is included in nep-ecm, nep-ets and nep-rmg
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