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Abstract:
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We propose a new class of copulas which is a generalization of conditional independence models. In these models, dependence among observed variables is modeled using one or several unobserved factors. Conditional on these factors, the distribution of these variables is given by the Gaussian copula. This structure allows one to build flexible and parsimonious models for data with complex dependence structures, such as data with spatial or temporal dependence, or to construct copulas with dynamic dependencies. With different choices of the factors one can obtain tail dependence and/or asymmetry, and parameter estimation is quite fast even in high dimensions when using the maximum likelihood approach. We show some interesting special cases of the proposed class of copulas and illustrate ideas with an empirical study.
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