Dependence Modeling with Copulas

This book covers recent advances in the field, including vine copula modeling of high-dimensional data. The author develops vine copula models and generalizations, discusses other multivariate constructions and parametric copula families, and presents dependence and tail properties to assist readers in copula model selection. He also covers inference, diagnostics, model comparison, numerical methods, and algorithms for copula applications. Software and code area available on the author’s website.

Dependence Modeling with Copulas covers 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.