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Dynamic copula quantile regressions and tail area dynamic dependence in Forex markets

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  • Eric Bouye
  • Mark Salmon

Abstract

We introduce a general approach to nonlinear quantile regression modelling based on the copula function that defines the dependency structure between the variables of interest. Hence, we extend Koenker and Bassett's (1978. Regression quantiles. Econometrica, 46, no. 1: 33-50.) original statement of the quantile regression problem by determining a distribution for the dependent variable Y conditional on the regressors X, and hence the specification of the quantile regression functions. The approach exploits the fact that the joint distribution function can be split into two parts: the marginals and the dependence function (or copula). We then deduce the form of the (invariably nonlinear) conditional quantile relationship implied by the copula. This can be achieved with arbitrary distributions assumed for the marginals. Some properties of the copula-based quantiles or c-quantiles are derived. Finally, we examine the conditional quantile dependency in the foreign exchange market and compare our quantile approach with standard tail area dependency measures.

Suggested Citation

  • Eric Bouye & Mark Salmon, 2009. "Dynamic copula quantile regressions and tail area dynamic dependence in Forex markets," The European Journal of Finance, Taylor & Francis Journals, vol. 15(7-8), pages 721-750.
  • Handle: RePEc:taf:eurjfi:v:15:y:2009:i:7-8:p:721-750
    DOI: 10.1080/13518470902853491
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    References listed on IDEAS

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    1. Moshe Buchinsky, 1998. "Recent Advances in Quantile Regression Models: A Practical Guideline for Empirical Research," Journal of Human Resources, University of Wisconsin Press, vol. 33(1), pages 88-126.
    2. Robert F. Engle & Simone Manganelli, 2004. "CAViaR: Conditional Autoregressive Value at Risk by Regression Quantiles," Journal of Business & Economic Statistics, American Statistical Association, vol. 22, pages 367-381, October.
    3. Koenker,Roger, 2005. "Quantile Regression," Cambridge Books, Cambridge University Press, number 9780521845731.
    4. Chen, Xiaohong & Fan, Yanqin, 2006. "Estimation of copula-based semiparametric time series models," Journal of Econometrics, Elsevier, vol. 130(2), pages 307-335, February.
    5. 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.
    6. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
    7. Powell, James L., 1986. "Censored regression quantiles," Journal of Econometrics, Elsevier, vol. 32(1), pages 143-155, June.
    8. Koenker, Roger & Park, Beum J., 1996. "An interior point algorithm for nonlinear quantile regression," Journal of Econometrics, Elsevier, vol. 71(1-2), pages 265-283.
    9. Mark Salmon & Nicolas Gaussel & Eric Bouy?, 2001. "Investigating Dynamic Dependence Using Copulae," Working Papers wp01-03, Warwick Business School, Finance Group.
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    Citations

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    Cited by:

    1. Lee, Tae-Hwy & Yang, Weiping, 2014. "Granger-causality in quantiles between financial markets: Using copula approach," International Review of Financial Analysis, Elsevier, vol. 33(C), pages 70-78.
    2. Beare, Brendan K., 2012. "Archimedean Copulas And Temporal Dependence," Econometric Theory, Cambridge University Press, vol. 28(06), pages 1165-1185, December.
    3. CORONEO, Laura & VEREDAS, David, 2006. "Intradaily seasonality of returns distribution. A quantile regression approach and intradaily VaR estimation," CORE Discussion Papers 2006077, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    4. Khalid Almeshal & Nader Naifar, 2016. "A quantile regression approach and nonlinear analysis with Archimedean copulas to explain the movements of residential real estate prices," Afro-Asian Journal of Finance and Accounting, Inderscience Enterprises Ltd, vol. 6(4), pages 374-395.
    5. Kraus, Daniel & Czado, Claudia, 2017. "D-vine copula based quantile regression," Computational Statistics & Data Analysis, Elsevier, vol. 110(C), pages 1-18.
    6. Chen, Xiaohong & Fan, Yanqin, 2006. "Estimation of copula-based semiparametric time series models," Journal of Econometrics, Elsevier, vol. 130(2), pages 307-335, February.
    7. Beare, Brendan K. & Seo, Juwon, 2014. "Time Irreversible Copula-Based Markov Models," Econometric Theory, Cambridge University Press, vol. 30(05), pages 923-960, October.
    8. Sim, Nicholas, 2016. "Modeling the dependence structures of financial assets through the Copula Quantile-on-Quantile approach," International Review of Financial Analysis, Elsevier, vol. 48(C), pages 31-45.
    9. Xiaohong Chen & Wei Biao Wu Wu & Yanping Yi, 2009. "Efficient estimation of copula-based semiparametric Markov models," CeMMAP working papers CWP06/09, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    10. Refk Selmi & Christos Kollias & Stephanos Papadamou & Rangan Gupta, 2017. "A Copula-Based Quantile-on-Quantile Regression Approach to Modeling Dependence Structure between Stock and Bond Returns: Evidence from Historical Data of India, South Africa, UK and US," Working Papers 201747, University of Pretoria, Department of Economics.
    11. Huo, Lijuan & Kim, Tae-Hwan & Kim, Yunmi, 2012. "Robust estimation of covariance and its application to portfolio optimization," Finance Research Letters, Elsevier, vol. 9(3), pages 121-134.
    12. David E. Allen & Abhay K. Singh & Robert J. Powell & Michael McAleer & James Taylor & Lyn Thomas, 2013. "Return-Volatility Relationship: Insights from Linear and Non-Linear Quantile Regression," Tinbergen Institute Discussion Papers 13-020/III, Tinbergen Institute.
    13. Reboredo, Juan C. & Ugolini, Andrea, 2016. "Quantile dependence of oil price movements and stock returns," Energy Economics, Elsevier, vol. 54(C), pages 33-49.
    14. Fabrizio Cipollini & Giampiero Gallo & Andrea Ugolini, 2016. "Median Response to Shocks: A Model for VaR Spillovers in East Asia," Econometrics Working Papers Archive 2016_01, Universita' degli Studi di Firenze, Dipartimento di Statistica, Informatica, Applicazioni "G. Parenti".
    15. Agbeyegbe, Terence D., 2015. "An inverted U-shaped crude oil price return-implied volatility relationship," Review of Financial Economics, Elsevier, vol. 27(C), pages 28-45.
    16. repec:eee:stapro:v:128:y:2017:i:c:p:14-20 is not listed on IDEAS
    17. David E Allen & Abhay K Singh & Robert J Powell & Michael McAleer & James Taylor & Lyn Thomas, 2012. "The Volatility-Return Relationship:Insights from Linear and Non-Linear Quantile Regressions," KIER Working Papers 831, Kyoto University, Institute of Economic Research.
    18. Avdulaj Krenar & Barunik Jozef, 2017. "A semiparametric nonlinear quantile regression model for financial returns," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 21(1), pages 81-97, February.
    19. Sim, Nicholas & Zhou, Hongtao, 2015. "Oil prices, US stock return, and the dependence between their quantiles," Journal of Banking & Finance, Elsevier, vol. 55(C), pages 1-8.
    20. Komunjer, Ivana, 2013. "Quantile Prediction," Handbook of Economic Forecasting, Elsevier.
    21. Bernard, Carole & Czado, Claudia, 2015. "Conditional quantiles and tail dependence," Journal of Multivariate Analysis, Elsevier, vol. 138(C), pages 104-126.
    22. Patton, Andrew J., 2012. "A review of copula models for economic time series," Journal of Multivariate Analysis, Elsevier, vol. 110(C), pages 4-18.
    23. repec:eee:eneeco:v:66:y:2017:i:c:p:493-507 is not listed on IDEAS

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