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Analyzing dependent data with vine copulas. A practical guide with R. (English) Zbl 1425.62001
Lecture Notes in Statistics 222. Cham: Springer (ISBN 978-3-030-13784-7/pbk; 978-3-030-13785-4/ebook). xxix, 242 p. (2019).
From the cover of the book: “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.”
The book is very large structured in a preface, contents, 11 chapters (divided in 71 subchapters), references, index.
Chapter 1. Multivariate distributions and copulas; Chapter 2. Dependence measures; Chapter 3. Bivariate copula classes, their visualization, and estimation; Chapter 4. Pair copula decompositions and constructions; Chapter 5. Regular vines; Chapter 6. Simulating regular vine copulas and distributions; Chapter 7. Parameter estimation in simplified regular vine copulas; Chapter 8. Selection of regular vine copula models; Chapter 9. Comparing regular vine copula models; Chapter 10. Case study: dependence among German DAX stocks; Chapter 11. Recent developments in vine copula based modeling.
The R-code of all figures and tables can be found at http://www.statistics.ma.tum.de/personen/claudia-czado/r-code-to-analyzing-dependent-data-with-vinecopulas.
Every chapter finished with exercises (except Chapters 10 and 11). The bibliography contains 265 references and the index more than 200 items. The book can be recommend all readers, who are interested in this field and “who are interested in using copula-based models for multivariate data structures” (from the preface).

MSC:
62-02 Research exposition (monographs, survey articles) pertaining to statistics
62H05 Characterization and structure theory for multivariate probability distributions; copulas
62H12 Estimation in multivariate analysis
62P05 Applications of statistics to actuarial sciences and financial mathematics
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