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Full Description
This textbook provides a step-by-step introduction to the class of vine copulas, their statistical inference and applications. It focuses on statistical estimation and selection methods for vine copulas in data applications. These flexible copula models can successfully accommodate any form of tail dependence and are vital to many applications in finance, insurance, hydrology, marketing, engineering, chemistry, aviation, climatology and health.
The book explains the pair-copula construction principles underlying these statistical models and discusses how to perform model selection and inference. It also derives simulation algorithms and presents real-world examples to illustrate the methodological concepts. The book includes numerous exercises that facilitate and deepen readers' understanding, and demonstrates how the R package VineCopula can be used to explore and build statistical dependence models from scratch. In closing, the book provides insights into recent developments and open research questions in vine copula based modeling.
The book is intended for students as well as statisticians, data analysts and any other quantitatively oriented researchers who are new to the field of vine copulas. Accordingly, it provides the necessary background in multivariate statistics and copula theory for exploratory data tools, so that readers only need a basic grasp of statistics and probability.
Contents
Preface.- Multivariate Distributions and Copulas.- Dependence Measures.- Bivariate Copula Classes, Their Visualization and Estimation.- Pair Copula Decompositions and Constructions.- Regular Vines.- Simulating Regular Vine Copulas and Distributions.- Parameter Estimation in Regular Vine Copulas.- Selection of Regular Vine Copula Models.- Comparing Regular Vine Copula Models.- Case Study: Dependence Among German DAX Stocks.- Recent Developments in Vine Copula Based Modeling.- Indices.
