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E-raamat: Analyzing Dependent Data with Vine Copulas: A Practical Guide With R

  • Formaat: EPUB+DRM
  • Sari: Lecture Notes in Statistics 222
  • Ilmumisaeg: 14-May-2019
  • Kirjastus: Springer Nature Switzerland AG
  • Keel: eng
  • ISBN-13: 9783030137854
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Analyzing Dependent Data with Vine Copulas: A Practical Guide With RSuurem pilt
  • Formaat: EPUB+DRM
  • Sari: Lecture Notes in Statistics 222
  • Ilmumisaeg: 14-May-2019
  • Kirjastus: Springer Nature Switzerland AG
  • Keel: eng
  • ISBN-13: 9783030137854
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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.


1 Multivariate Distributions and Copulas
1(26)
1.1 Univariate Distributions
1(3)
1.2 Multivariate Distributions
4(6)
1.3 Features of Multivariate Data
10(1)
1.4 The Concept of a Copula and Sklar's Theorem
11(4)
1.5 Elliptical Copulas
15(2)
1.6 Empirical Copula Approximation
17(1)
1.7 Invariance Properties of Copulas
18(1)
1.8 Meta Distributions
19(1)
1.9 Bivariate Conditional Distributions Expressed in Terms of Their Copulas
20(2)
1.10 Exercises
22(5)
2 Dependence Measures
27(16)
2.1 Pearson Product-Moment Correlation
27(1)
2.2 Kendall's τ and Spearman's ρs
28(6)
2.3 Tail Dependence
34(2)
2.4 Partial and Conditional Correlations
36(3)
2.5 Exercises
39(4)
3 Bivariate Copula Classes, Their Visualization, and Estimation
43(34)
3.1 Construction of Bivariate Copula Classes
43(1)
3.2 Bivariate Elliptical Copulas
43(1)
3.3 Archimedean Copulas
43(4)
3.4 Bivariate Extreme-Value Copulas
47(6)
3.5 Relationship Between Copula Parameters and Kendall's τ
53(3)
3.6 Rotated and Reflected Copulas
56(2)
3.7 Relationship Between Copula Parameters and Tail Dependence Coefficients
58(1)
3.8 Exploratory Visualization
58(4)
3.9 Simulation of Bivariate Copula Data
62(2)
3.10 Parameter Estimation in Bivariate Copula Models
64(3)
3.11 Conditional Bivariate Copulas
67(3)
3.12 Average Conditional and Partial Bivariate Copulas
70(1)
3.13 Exercises
71(6)
4 Pair Copula Decompositions and Constructions
77(18)
4.1 Illustration in Three Dimensions
77(11)
4.2 Pair-Copula Constructions of Drawable D-vine and Canonical C-vine Distributions
88(2)
4.3 Conditional Distribution Functions Associated with Multivariate Distributions
90(2)
4.4 Exercises
92(3)
5 Regular Vines
95(28)
5.1 Necessary Graph Theoretic Background
95(3)
5.2 Regular Vine Tree Sequences
98(5)
5.3 Regular Vine Distributions and Copulas
103(5)
5.4 Simplified Regular Vine Classes
108(3)
5.5 Representing Regular Vines Using Regular Vine Matrices
111(8)
5.6 Exercises
119(4)
6 Simulating Regular Vine Copulas and Distributions
123(22)
6.1 Simulating Observations from Multivariate Distributions
123(1)
6.2 Simulating from Pair Copula Constructions
124(3)
6.3 Simulating from C-vine Copulas
127(6)
6.4 Simulating from D-vine Copulas
133(3)
6.5 Simulating from Regular Vine Copulas
136(7)
6.6 Exercises
143(2)
7 Parameter Estimation in Simplified Regular Vine Copulas
145(10)
7.1 Likelihood of Simplified Regular Vine Copulas
145(2)
7.2 Sequential and Maximum Likelihood Estimation in Simplified Regular Vine Copulas
147(2)
7.3 Asymptotic Theory of Parametric Regular Vine Copula Estimators
149(3)
7.4 Exercises
152(3)
8 Selection of Regular Vine Copula Models
155(18)
8.1 Selection of a Parametric Copula Family for Each Pair Copula Term and Estimation of the Corresponding Parameters for a Given Vine Tree Structure
156(2)
8.2 Selection and Estimation of all Three Model Components of a Vine Copula
158(1)
8.3 The Dißmann Algorithm for Sequential Top-Down Selection of Vine Copulas
159(10)
8.4 Exercises
169(4)
9 Comparing Regular Vine Copula Models
173(12)
9.1 Akaike and Bayesian Information Criteria for Regular Vine Copulas
174(3)
9.2 Kullback-Leibler Criterion
177(1)
9.3 Vuong Test for Comparing Different Regular Vine Copula Models
178(4)
9.3.1 Correction Factors in the Vuong Test for Adjusting for Model Complexity
181(1)
9.4 Exercises
182(3)
10 Case Study: Dependence Among German DAX Stocks
185(18)
10.1 Data Description and Sector Groupings
185(2)
10.2 Marginal Models
187(1)
10.3 Finding Representatives of Sectors
188(1)
10.4 Dependence Structure Among Representatives
188(11)
10.5 Model Comparison
199(2)
10.6 Some Interpretive Remarks
201(2)
11 Recent Developments in Vine Copula Based Modeling
203(24)
11.1 Advances in Estimation
203(4)
11.2 Advances in Model Selection of Vine Copula Based Models
207(6)
11.3 Advances for Special Data Structures
213(4)
11.4 Applications of Vine Copulas in Financial Econometrics
217(2)
11.5 Applications of Vine Copulas in the Life Sciences
219(3)
11.6 Application of Vine Copulas in Insurance
222(1)
11.7 Application of Vine Copulas in the Earth Sciences
222(1)
11.8 Application of Vine Copulas in Engineering
223(1)
11.9 Software for Vine Copula Modeling
223(4)
References 227(12)
Index 239
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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