Dynamic Copula Processes

Abstract

This paper presents a flexible new family of copula-based multivariate models designed for handling large numbers of variables (1) as random vectors in the static case or (2) as vector stochastic processes in the dynamic case. The family includes models with upper and lower tail dependence. Variables need not be exchangeable. To illustrate the model’s potential; three radically different examples have been constructed: a straight additive model, an additive conditional gamma model and a switching model. Archimedean copulas turn out to be a special case of the general model. Another advantage of these models it that it is easy to construct dynamic versions of the static copulas. Lastly, as these models are defined in a conditional independence framework, they are easy to simulate.

Keywords: Key words: Copulas, Archimedean, Tail dependence, Pearson process, Affine processes, CIR process, multivariate Laplace transform