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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.

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Bibliographic Info

Article provided by Taylor & Francis Journals in its journal The European Journal of Finance.

Volume (Year): 15 (2009)
Issue (Month): 7-8 ()
Pages: 721-750

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Handle: RePEc:taf:eurjfi:v:15:y:2009:i:7-8:p:721-750

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Related research

Keywords: Copula; Quantile; Regression; dependence; foreign exchange markets;

References

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  1. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
  2. 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.
  3. Chen, Xiaohong & Fan, Yanqin, 2006. "Estimation of copula-based semiparametric time series models," Journal of Econometrics, Elsevier, vol. 130(2), pages 307-335, February.
  4. Roger Koenker & Kevin F. Hallock, 2001. "Quantile Regression," Journal of Economic Perspectives, American Economic Association, vol. 15(4), pages 143-156, Fall.
  5. 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.
  6. Powell, James L., 1986. "Censored regression quantiles," Journal of Econometrics, Elsevier, vol. 32(1), pages 143-155, June.
  7. 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.
  8. Mark Salmon & Nicolas Gaussel & Eric Bouy?, 2001. "Investigating Dynamic Dependence Using Copulae," Working Papers wp01-03, Warwick Business School, Finance Group.
  9. 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, 05.
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Citations

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Cited by:
  1. 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.
  2. Xiaohong Chen & Yanqin Fan, 2002. "Estimation of Copula-Based Semiparametric Time Series Models," Vanderbilt University Department of Economics Working Papers 0226, Vanderbilt University Department of Economics, revised Oct 2004.
  3. Chen, Xiaohong & Fan, Yanqin, 2006. "Estimation of copula-based semiparametric time series models," Journal of Econometrics, Elsevier, vol. 130(2), pages 307-335, February.
  4. Beare, Brendan K. & Seo, Juwon, 2012. "Time irreversible copula-based Markov Models," University of California at San Diego, Economics Working Paper Series qt31f8500p, Department of Economics, UC San Diego.
  5. Beare, Brendan K., 2010. "Archimedean Copulas and Temporal Dependence," University of California at San Diego, Economics Working Paper Series qt0xh8q1g3, Department of Economics, UC San Diego.
  6. Xiaohong Chen & Wei Biao 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.
  7. 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.
  8. 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.
  9. 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.

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