Structured factor copula models: Theory, inference and computation

In factor copula models for multivariate data, dependence is explained via one or several common factors. These models are flexible in handling tail dependence and asymmetry with parsimonious dependence structures. We propose two structured factor copula models for the case where variables can be split into non-overlapping groups such that there is homogeneous dependence within each group. A typical example of such variables occurs for stock returns from different sectors. The structured models inherit most of dependence properties derived for common factor copula models. With appropriate numerical methods, efficient estimation of dependence parameters is possible for data sets with over 100 variables. We apply the structured factor copula models to analyze a financial data set, and compare with other copula models for tail inference. Using model-based interval estimates, we find that some commonly used risk measures may not be well discriminated by copula models, but tail-weighted dependence measures can discriminate copula models with different dependence and tail properties.