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Change analysis of a dynamic copula for measuring dependence in multivariate financial data

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  • Dominique Guegan

    (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement)

  • Jing Zhang

    (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, ECNU - East China Normal University [Shangaï])

Abstract

This paper proposes a new approach to measure the dependence in multivariate financial data. Data in finance and insurance often cover a long time period. Therefore, the economic factors may induce some changes inside the dependence structure. Recently, two methods using copulas have been proposed to analyze such changes. The first approach investigates the changes of copula's parameters. The second one tests the changes of copulas by determining the best copulas using moving windows. In this paper we take into account the non stationarity of the data and analyze : (1) the changes of parameters while the copula family keeps static ; (2) the changes of copula family. We propose a series of tests based on conditional copulas and goodness-of-fit (GOF) tests to decide the type of change, and further give the corresponding change analysis. We illustrate our approach with Standard & Poor 500 and Nasdaq indices, and provide dynamic risk measures.

Suggested Citation

  • Dominique Guegan & Jing Zhang, 2010. "Change analysis of a dynamic copula for measuring dependence in multivariate financial data," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00368334, HAL.
    • Handle: RePEc:hal:cesptp:halshs-00368334
    DOI: 10.1080/14697680902933041
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-00368334
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    1. Dominique Guégan, 2007. "Global and local stationary modelling in finance: theory and empirical evidence," Documents de travail du Centre d'Economie de la Sorbonne b07053, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    2. Dominique Guegan & Jing Zang, 2009. "Pricing bivariate option under GARCH-GH model with dynamic copula: application for Chinese market," The European Journal of Finance, Taylor & Francis Journals, vol. 15(7-8), pages 777-795.
    3. Granger, Clive W.J. & Terasvirta, Timo & Patton, Andrew J., 2006. "Common factors in conditional distributions for bivariate time series," Journal of Econometrics, Elsevier, vol. 132(1), pages 43-57, May.
    4. Cyril Caillault & Dominique Guegan, 2005. "Empirical estimation of tail dependence using copulas: application to Asian markets," Quantitative Finance, Taylor & Francis Journals, vol. 5(5), pages 489-501.
    5. Fermanian, Jean-David, 2005. "Goodness-of-fit tests for copulas," Journal of Multivariate Analysis, Elsevier, vol. 95(1), pages 119-152, July.
    6. Cyril Caillault, Dominique Guégan, 2009. "Forecasting VaR and Expected Shortfall Using Dynamical Systems: A Risk Management Strategy," Frontiers in Finance and Economics, SKEMA Business School, vol. 6(1), pages 26-50, April.
    7. Andrew J. Patton, 2006. "Modelling Asymmetric Exchange Rate Dependence," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 47(2), pages 527-556, May.
    8. Jondeau, Eric & Rockinger, Michael, 2006. "The Copula-GARCH model of conditional dependencies: An international stock market application," Journal of International Money and Finance, Elsevier, vol. 25(5), pages 827-853, August.
    9. Gombay, Edit & Horváth, Lajos, 1996. "On the Rate of Approximations for Maximum Likelihood Tests in Change-Point Models," Journal of Multivariate Analysis, Elsevier, vol. 56(1), pages 120-152, January.
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    Cited by:

    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. Matteo Iacopini & Dominique Guégan, 2018. "Nonparametric Forecasting of Multivariate Probability Density Functions," Working Papers 2018:15, Department of Economics, University of Venice "Ca' Foscari".
    3. Dominique Guegan & Jing Zang, 2009. "Pricing bivariate option under GARCH-GH model with dynamic copula: application for Chinese market," The European Journal of Finance, Taylor & Francis Journals, vol. 15(7-8), pages 777-795.
    4. Dominique Guegan, 2007. "La persistance dans les marchés financiers," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00179269, HAL.
    5. Zhu, Bo & Lin, Renda & Deng, Yuanyue & Chen, Pingshe & Chevallier, Julien, 2021. "Intersectoral systemic risk spillovers between energy and agriculture under the financial and COVID-19 crises," Economic Modelling, Elsevier, vol. 105(C).
    6. Dominique Guegan & Jing Zhang, 2009. "Pricing bivariate option under GARCH-GH model with dynamic copula: application for Chinese market," PSE-Ecole d'économie de Paris (Postprint) halshs-00368336, HAL.
    7. Aepli, Matthias D. & Füss, Roland & Henriksen, Tom Erik S. & Paraschiv, Florentina, 2017. "Modeling the multivariate dynamic dependence structure of commodity futures portfolios," Journal of Commodity Markets, Elsevier, vol. 6(C), pages 66-87.
    8. Li, Jie & Li, Ping, 2021. "Empirical analysis of the dynamic dependence between WTI oil and Chinese energy stocks," Energy Economics, Elsevier, vol. 93(C).
    9. Dominique Guegan & Matteo Iacopini, 2018. "Nonparametric forecasting of multivariate probability density functions," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-01821815, HAL.
    10. Aepli, Matthias D. & Frauendorfer, Karl & Fuess, Roland & Paraschiv, Florentina, 2015. "Multivariate Dynamic Copula Models: Parameter Estimation and Forecast Evaluation," Working Papers on Finance 1513, University of St. Gallen, School of Finance.
    11. Zhu, Xiaoqian & Xie, Yongjia & Li, Jianping & Wu, Dengsheng, 2015. "Change point detection for subprime crisis in American banking: From the perspective of risk dependence," International Review of Economics & Finance, Elsevier, vol. 38(C), pages 18-28.
    12. Yali Dou & Haiyan Liu & Georgios Aivaliotis, 2019. "Dynamic Dependence Modeling in financial time series," Papers 1908.05130, arXiv.org.
    13. Matthias R. Fengler & Ostap Okhrin, 2012. "Realized Copula," SFB 649 Discussion Papers SFB649DP2012-034, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    14. Dominique Guégan, 2009. "A Meta-Distribution for Non-Stationary Samples," CREATES Research Papers 2009-24, Department of Economics and Business Economics, Aarhus University.
    15. Dominique Guegan & Jing Zhang, 2009. "Pricing bivariate option under GARCH-GH model with dynamic copula: application for Chinese market," Post-Print halshs-00368336, HAL.
    16. Dominique Guegan & Jing Zhang, 2007. "Pricing bivariate option under GARCH-GH model with dynamic copula : application for Chinese market," Post-Print halshs-00188248, HAL.
    17. Rémillard, Bruno & Papageorgiou, Nicolas & Soustra, Frédéric, 2012. "Copula-based semiparametric models for multivariate time series," Journal of Multivariate Analysis, Elsevier, vol. 110(C), pages 30-42.
    18. Bing-Yue Liu & Qiang Ji & Ying Fan, 2017. "A new time-varying optimal copula model identifying the dependence across markets," Quantitative Finance, Taylor & Francis Journals, vol. 17(3), pages 437-453, March.
    19. Dominique Guegan & Matteo Iacopini, 2018. "Nonparametric forecasting of multivariate probability density functions," Post-Print halshs-01821815, HAL.
    20. Dominique Guégan & Matteo Iacopini, 2018. "Nonparameteric forecasting of multivariate probability density functions," Documents de travail du Centre d'Economie de la Sorbonne 18012, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    21. Florian Stark & Sven Otto, 2020. "Testing and Dating Structural Changes in Copula-based Dependence Measures," Papers 2011.05036, arXiv.org.
    22. Okyoung Na & Jiyeon Lee & Sangyeol Lee, 2013. "Change point detection in SCOMDY models," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 97(3), pages 215-238, July.

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    More about this item

    Keywords

    Dynamic copula; goodness-of-fit test; change-point; time-varying parameter; VaR; ES;
    All these keywords.

    JEL classification:

    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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