# Analyzing Dependent Data with Vine Copulas

## A Practical Guide With R

Textbook

Part of the Lecture Notes in Statistics book series (LNS, volume 222)

1. Front Matter
Pages i-xxix
Pages 1-25
Pages 27-41
Pages 43-75
Pages 77-93
Pages 95-122
Pages 123-144
Pages 145-153
Pages 155-171
Pages 173-184
Pages 185-201
Pages 203-226
13. Back Matter
Pages 227-242

### Introduction

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.

### Keywords

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

#### Authors and affiliations

• 1
1. 1.Department of MathematicsTechnical University of MunichGarchingGermany

### Bibliographic information

• DOI https://doi.org/10.1007/978-3-030-13785-4
• Copyright Information Springer Nature Switzerland AG 2019
• Publisher Name Springer, Cham
• eBook Packages Mathematics and Statistics
• Print ISBN 978-3-030-13784-7
• Online ISBN 978-3-030-13785-4
• Series Print ISSN 0930-0325
• Series Online ISSN 2197-7186
• Buy this book on publisher's site