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Multivariate Reflection Symmetry of Copula Functions

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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

Suggested Citation

  • Monica Billio & Lorenzo Frattarolo & Dominique Guegan, 2017. "Multivariate Reflection Symmetry of Copula Functions," Documents de travail du Centre d'Economie de la Sorbonne 17033, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    • Handle: RePEc:mse:cesdoc:17033
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    More about this item

    Keywords

    Dependence Asymmetry; Copula; Reflection Symmetry; Radial Symmetry; Empirical Process; Dependent Multiplier Bootstrap; Financial Stress;
    All these keywords.

    JEL classification:

    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • C40 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - General
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection

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