Modelling Time-Varying Exchange Rate Dependence Using the Conditional Copula

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.