Multivariate Reflection Symmetry of Copula Functions

Abstract : We propose a multivariate nonparametric copula test of reflection symmetry. The test is valid in any number of dimensions, extending previous results that cover the bivariate case. Furthermore, the asymptotic theory for the test relies on recent results on the dependent multiplier bootstrap, valid for sub-exponentially strongly mixing data. Consequently to the introduction of those two features, the procedure is suitable for financial time series whose asymmetric dependence, in distressed periods, has already been documented elsewhere. We conduct an extensive simulation study of empirical size and power and provide several examples of applications. In particular, we investigate the use of the statistic as a financial stress indicator by comparing it with the CISS, the leading ECB indicator.
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Monica Billio, Lorenzo Frattarolo, Dominique Guégan. Multivariate Reflection Symmetry of Copula Functions. 2017. ⟨halshs-01592147⟩

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