Modeling Dependence in High Dimensions: A Factor Copula Approach

In this paper we study the dependence structure, or copula, of a large set of economic variables. We employ recently proposed factor copula models, that offer a flexible, parsimonious approach to high-dimensional applications. We augment the factor copula models with Markov-switching dynamics to allow for time-varying dependence, resulting in a more realistic model specification. We apply the models to daily returns on 101 constituents of the S&P 100 equity index and find that a model that allows for non-normal features of dependence is needed to adequately model the dependence structure of the returns. Specifically, we show that the returns display heterogeneous dependence, tail dependence and asymmetric dependence. Furthermore, we find strong evidence of regime shifts in the dependence structure, where periods of high dependence seem to alternate with periods of substantially less dependence between the asset returns.