This book introduces the main theoretical findings related to copulas and shows how statistical modeling of multivariate continuous distributions using copulas can be carried out in the R statistical environment with the package copula (among others). Copulas are multivariate distribution functions with standard uniform univariate margins. They are increasingly applied to modeling dependence among random variables in fields such as risk management, actuarial science, insurance, finance, engineering, hydrology, climatology, and meteorology, to name a few. In the spirit of the Use R! series, each chapter combines key theoretical definitions or results with illustrations in R. Aimed at statisticians, actuaries, risk managers, engineers and environmental scientists wanting to learn about the theory and practice of copula modeling using R without an overwhelming amount of mathematics, the book can also be used for teaching a course on copula modeling.
... of the copula C of the random vector X. We will investigate its properties and consider examples for selected copulas. ... Section 3.3.2 focuses on a related measure of multivariate association, namely Pearson's Phi-Square.
The book explains the pair-copula construction principles underlying these statistical models and discusses how to perform model selection and inference.
Patton, A. J. (2004): On the out-of-sample importance of skewness and asymmetric dependence for asset allocation, Journal of Financial Econometrics, 2(1), pp. 130–168. ... Empirical process techniques for dependent data, pp. 345–364.
Alternatively, Copulas are a more flexible dependence measurement. This book focuses on the development of Dynamic Copula frameworks by implementing stochastic parameters into Archimedian and Elliptical Copula functions.