Post by Sapphire Capital on Jul 23, 2008 21:21:03 GMT 4
Dynamic Copula Quantile Regressions and Tail Area Dynamic Dependence in Forex Markets
MARK SALMON
University of Warwick - Warwick Business School
ERIC BOUYE
affiliation not provided to SSRN
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May 5, 2008
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] 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 non linear) 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 conditional quantile dependency in the foreign exchange market and compare our quantile approach with standard tail area dependency measures.
papers.ssrn.com/sol3/Delivery.cfm/SSRN_ID1129855_code358995.pdf?abstractid=1129855&mirid=3
MARK SALMON
University of Warwick - Warwick Business School
ERIC BOUYE
affiliation not provided to SSRN
--------------------------------------------------------------------------------
May 5, 2008
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] 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 non linear) 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 conditional quantile dependency in the foreign exchange market and compare our quantile approach with standard tail area dependency measures.
papers.ssrn.com/sol3/Delivery.cfm/SSRN_ID1129855_code358995.pdf?abstractid=1129855&mirid=3