Modelling Dependence in High Dimensions with Factor Copulas

This paper presents new models for the dependence structure, or copula, of economic variables, and asymptotic results for new simulation-based estimators of these models. The proposed models are based on a factor structure for the copula and are particularly attractive for high dimensional applications, involving …fty or more variables. Estimation of this class of models is complicated by the lack of a closed-form likelihood, but estimation via a simulation-based method using rank statistics is simple, and we provide asymptotic results that show the consistency and asymptotic normality of such estimators. We analyze the …nite-sample behavior of these estimators in an extensive simulation study. We apply the model to a group of 100 daily stock returns and …nd evidence of statistically signi…cant tail dependence, and that the dependence between these assets is stronger in crashes than booms.