Modelling Time-Varying Exchange Rate Dependence Using the Conditional Copula

UCSD Discussion Paper No. 01-09

52 Pages Posted: 24 Jul 2001

See all articles by Andrew J. Patton

Andrew J. Patton

Duke University - Department of Economics

Date Written: June 2001


Linear correlation is only an adequate means of describing the dependence between two random variables when they are jointly elliptically distributed. When the joint distribution of two or more variables is not elliptical the linear correlation coefficient becomes just one of many possible ways of summarising the dependence structure between the variables. In this paper we make use of a theorem due to Sklar (1959), which shows that an n-dimensional distribution function may be decomposed into its n marginal distributions, and a copula, which completely describes the dependence between the n variables. We verify that Sklar's theorem may be extended to conditional distributions, and apply it to the modelling of the time-varying joint distribution of the Deutsche mark-U.S. dollar and Yen-U.S. dollar exchange rate returns. We find evidence that the conditional dependence between these exchange rates is time-varying, and that it is asymmetric: dependence is greater during appreciations of the U.S. dollar against the mark and the yen than during depreciations of the U.S. dollar. We also find strong evidence of a structural break in the conditional copula following the introduction of the euro.

Keywords: time series, copulas, dependence, exchange rates

JEL Classification: C32, C51, C52, F31

Suggested Citation

Patton, Andrew J., Modelling Time-Varying Exchange Rate Dependence Using the Conditional Copula (June 2001). UCSD Discussion Paper No. 01-09, Available at SSRN: or

Andrew J. Patton (Contact Author)

Duke University - Department of Economics ( email )

213 Social Sciences Building
Box 90097
Durham, NC 27708-0204
United States