Probability Density Decomposition for Conditionally Dependent Random Variables Modeled by Vines
Annals of Mathematics and Artificial Intelligence
Tail dependence functions and vine copulas
Journal of Multivariate Analysis
Tail order and intermediate tail dependence of multivariate copulas
Journal of Multivariate Analysis
Vine copulas with asymmetric tail dependence and applications to financial return data
Computational Statistics & Data Analysis
Selecting and estimating regular vine copulae and application to financial returns
Computational Statistics & Data Analysis
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General conditional independence models for d observed variables, in terms of p latent variables, are presented in terms of bivariate copulas that link observed data to latent variables. The representation is called a factor copula model and the classical multivariate normal model with a correlation matrix having a factor structure is a special case. Dependence and tail properties of the model are obtained. The factor copula model can handle multivariate data with tail dependence and tail asymmetry, properties that the multivariate normal copula does not possess. It is a good choice for modeling high-dimensional data as a parametric form can be specified to have O(d) dependence parameters instead of O(d^2) parameters. Data examples show that, based on the Akaike information criterion, the factor copula model provides a good fit to financial return data, in comparison with related truncated vine copula models.