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Multivariate Reflection Symmetry of Copula Functions

Author

Listed:
  • Monica Billio

    (University of Ca’ Foscari [Venice, Italy])

  • Lorenzo Frattarolo

    (University of Ca’ Foscari [Venice, Italy])

  • Dominique Guegan

    (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, Labex ReFi - UP1 - Université Paris 1 Panthéon-Sorbonne)

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," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-01592147, HAL.
    • Handle: RePEc:hal:cesptp:halshs-01592147
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-01592147
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    References listed on IDEAS

    as
    1. Bücher, Axel & Ruppert, Martin, 2013. "Consistent testing for a constant copula under strong mixing based on the tapered block multiplier technique," Journal of Multivariate Analysis, Elsevier, vol. 116(C), pages 208-229.
    2. Chen, Yi-Ting, 2007. "Moment-Based Copula Tests for Financial Returns," Journal of Business & Economic Statistics, American Statistical Association, vol. 25, pages 377-397, October.
    3. Azam Dehgani & Ali Dolati & Manuel Úbeda-Flores, 2013. "Measures of radial asymmetry for bivariate random vectors," Statistical Papers, Springer, vol. 54(2), pages 271-286, May.
    4. Kremer, Manfred & Lo Duca, Marco & Holló, Dániel, 2012. "CISS - a composite indicator of systemic stress in the financial system," Working Paper Series 1426, European Central Bank.
    5. Daniel Berg & Jean‐François Quessy, 2009. "Local Power Analyses of Goodness‐of‐fit Tests for Copulas," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 36(3), pages 389-412, September.
    6. repec:ecb:ecbwps:20111426 is not listed on IDEAS
    7. Schmid, Friedrich & Schmidt, Rafael, 2007. "Multivariate extensions of Spearman's rho and related statistics," Statistics & Probability Letters, Elsevier, vol. 77(4), pages 407-416, February.
    8. Carabarin-Aguirre, Alberto & Ivanoff, B. Gail, 2010. "Estimation of a distribution under generalized censoring," Journal of Multivariate Analysis, Elsevier, vol. 101(6), pages 1501-1519, July.
    9. Ang, Andrew & Chen, Joseph, 2002. "Asymmetric correlations of equity portfolios," Journal of Financial Economics, Elsevier, vol. 63(3), pages 443-494, March.
    10. Masaaki Sibuya, 1959. "Bivariate extreme statistics, I," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 11(2), pages 195-210, June.
    11. Kojadinovic, Ivan & Yan, Jun, 2010. "Modeling Multivariate Distributions with Continuous Margins Using the copula R Package," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 34(i09).
    12. Bücher, Axel & Volgushev, Stanislav, 2013. "Empirical and sequential empirical copula processes under serial dependence," Journal of Multivariate Analysis, Elsevier, vol. 119(C), pages 61-70.
    13. Jean-François Quessy, 2012. "Testing for Bivariate Extreme Dependence Using Kendall's Process," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 39(3), pages 497-514, September.
    14. Carrasco, Marine & Chen, Xiaohong, 2002. "Mixing And Moment Properties Of Various Garch And Stochastic Volatility Models," Econometric Theory, Cambridge University Press, vol. 18(1), pages 17-39, February.
    15. Harder, Michael & Stadtmüller, Ulrich, 2014. "Maximal non-exchangeability in dimension d," Journal of Multivariate Analysis, Elsevier, vol. 124(C), pages 31-41.
    16. Bucher, Axel & Kojadinovic, Ivan, 2013. "A dependent multiplier bootstrap for the sequential empirical copula process under strong mixing," LIDAM Discussion Papers ISBA 2013029, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    17. Segers, Johan, 2012. "Asymptotics of empirical copula processes under non-restrictive smoothness assumptions," LIDAM Reprints ISBA 2012009, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    18. Dimitris Politis & Halbert White, 2004. "Automatic Block-Length Selection for the Dependent Bootstrap," Econometric Reviews, Taylor & Francis Journals, vol. 23(1), pages 53-70.
    19. François Longin & Bruno Solnik, 2001. "Extreme Correlation of International Equity Markets," Journal of Finance, American Finance Association, vol. 56(2), pages 649-676, April.
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    More about this item

    Keywords

    Financial Stress; Radial Symmetry; Reflection Symmetry; Copula; Dependence Asymmetry; Empirical Process; Dependent Multiplier Bootstrap;
    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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