Clustering Dependencies Via Mixtures of Copulas

Abstract

The use of mixture models for clustering purposes has been considerably increased the last years primarily due to the existence of efficient computational methods that facilitate estimation. Nowadays, there are several clustering procedures based on mixtures for certain types of data. On the other hand, copulas are becoming very popular models to model dependencies as one of their appealing properties is the separation of the marginal properties of the data from the dependence properties. The purpose of this article is to put together the two distinct ideas, namely mixtures and copulas, so as to use mixtures of copulas aiming at using them for clustering with respect to the dependence properties of the data. This is accomplished by considering finite mixture of different copulas to represent different dependence structures. We provide properties of the derived models along with the description of an estimation method using an EM algorithm based on the standard approach for mixture models. Using daily returns from major stock markets, we illustrate the potential of our method.