Analyzing Dependent Data with Vine Copulas

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.

• vine copulas
• dependence modelling
• copulas
• tail dependence
• multivariate statistics
• model selection
• R package VineCopula
• statistical inference for vine copulas
• dependent data
• dependence measures
• bivariate copula
• pair copula
• regular vine copula
• vine copula based modeling
• case study
• parameter estimation in copulas
• pair copula decomposition
• simulating regular vine copulas

• Department of Mathematics, Technical University of Munich, Garching, Germany

  Claudia Czado

Claudia Czado is an Associate Professor of Applied Mathematical Statistics at the Technical University of Munich, Germany. Her research interests are in the dependence modeling of complex data structures, copula based quantile regression, generalized linear models and computational Bayesian methods, and the applications of these methods. She holds a Ph.D. in Operations Research and Industrial Engineering from Cornell University, USA.

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