Interdependence across various exchange rates: A mixed copula approach

Abstract

The purpose of this thesis is to study the dependence structure of exchange rates pairs using a mixture of copula as opposed to a single copula approach. Mixed copula models have the ability to generate dependence structures that do not belong to existing copula families. The flexibility in choosing component copulas in this mixture model aids the construction of a system that is simultaneously parsimonious and flexible enough to generate most dependence patterns in exchange rate data. Furthermore, the method of mixture copulas facilitates the separation of both the structure and degree of dependence, concepts that are respectively embodied in two essential and distinct parameters for the study of dependence – the weight parameters and the association parameters. The model proposed was constructed to capture various dependence patterns using carefully chosen mixtures of Gaussian, Gumbel and Clayton copulas. We used a two stage semi-parametric approach by first estimating the marginal distributions of each exchange rate pair non-parametrically, and then plugging in the empirical CDF’s into the copula. The empirical findings of this experimental study shows a high tendency that each of the exchange rate pairs would either appreciate or depreciate together against the US dollars and that relationship is stronger than that implied by the Gaussian assumption. Our proposed copula mixture model therefore adequately represents the dependence function which appropriately captures the dependence structure between each of the exchange rate pairs in this experimental study. The implications for these findings will be useful for central bank’s monetary policies aimed at exchange rate price stabilization as well as for other stake holders in the exchange rates business. It can also be applied to a wide range of analysis in economics, finance, health, engineering, biology and other related disciplines.