Dependence Modeling with Copulas [Hardcover]

Dependence Modeling with Copulascovers the substantial advances that have taken place in the field during the last 15 years, including vine copula modeling of high-dimensional data. Vine copula models are constructed from a sequence of bivariate copulas. The book develops generalizations of vine copula models, including common and structured factor models that extend from the Gaussian assumption to copulas. It also discusses other multivariate constructions and parametric copula families that have different tail properties and presents extensive material on dependence and tail properties to assist in copula model selection.

The author shows how numerical methods and algorithms for inference and simulation are important in high-dimensional copula applications. He presents the algorithms as pseudocode, illustrating their implementation for high-dimensional copula models. He also incorporates results to determine dependence and tail properties of multivariate distributions for future constructions of copula models.

Introduction
Dependence modeling
Early research for multivariate non-Gaussian
Copula representation for a multivariate distribution
Data examples: scatterplots and semi-correlations
Likelihood analysis and model comparisons
Copula models versus alternative multivariate models
Terminology for multivariate distributions with U(0, 1) margins
Copula constructions and properties

Basics: Dependence, Tail Behavior, and Asymmetries
Multivariate cdfs and their conditional distributions
Laplace transforms
Extreme value theory
Tail heaviness
Probability integral transform
Multivariate Gaussian/normal
Elliptical and multivariate t distributions
Multivariate dependence concepts
Fr?chet classes and Fr?chet bounds, gil|