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

  • Eric Bouye
  • Mark Salmon

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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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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  1. Mark Salmon & Nicolas Gaussel & Eric Bouy?, 2001. "Investigating Dynamic Dependence Using Copulae," Working Papers wp01-03, Warwick Business School, Finance Group.
  2. Powell, James L., 1986. "Censored regression quantiles," Journal of Econometrics, Elsevier, vol. 32(1), pages 143-155, June.
  3. Andrew Patton, 2004. "Modelling Asymmetric Exchange Rate Dependence," Working Papers wp04-04, Warwick Business School, Finance Group.
  4. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
  5. Robert Engle & Simone Manganelli, 2000. "CAViaR: Conditional Autoregressive Value at Risk by Regression Quantiles," Econometric Society World Congress 2000 Contributed Papers 0841, Econometric Society.
  6. repec:cup:cbooks:9780521845731 is not listed on IDEAS
  7. Chen, Xiaohong & Fan, Yanqin, 2006. "Estimation of copula-based semiparametric time series models," Journal of Econometrics, Elsevier, vol. 130(2), pages 307-335, February.
  8. 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.
  9. Roger Koenker & Kevin F. Hallock, 2001. "Quantile Regression," Journal of Economic Perspectives, American Economic Association, vol. 15(4), pages 143-156, Fall.
  10. 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.
  11. repec:cup:cbooks:9780521608275 is not listed on IDEAS
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