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DEPENDENCE MODELING
Vine Copula Handbook
edited by Dorota Kurowicka (Delft University of Technology, The Netherlands) & Harry Joe (University of British Columbia, Canada)
This book is a collaborative effort from three workshops held over the last three years, all involving principal contributors to the vine-copula methodology. Research and applications in vines have been growing rapidly and there is now a growing need to collate basic results, and standardize terminology and methods. Specifically, this handbook will (1) trace historical developments, standardizing notation and terminology, (2) summarize results on bivariate copulae, (3) summarize results for regular vines, and (4) give an overview of its applications. In addition, many of these results are new and not readily available in any existing journals. New research directions are also discussed.
Contents:
Introduction: Dependence Modeling (D Kurowicka)
Multivariate Copulae (M Fischer)
Vines Arise (R M Cooke et al.)
Sampling Count Variables with Specified Pearson Correlation: A Comparison Between a Naive and a C-Vine Sampling Approach (V Erhardt & C Czado)
Micro Correlations and Tail Dependence (R M Cooke et al.)
The Copula Information Criterion and Its Implications for the Maximum Pseudo-Likelihood Estimator (S Grønneberg)
Dependence Comparisons of Vine Copulae with Four or More Variables (H Joe)
Tail Dependence in Vine Copulae (H Joe)
Counting Vines (O Morales-Nápoles)
Regular Vines: Generation Algorithm and Number of Equivalence Classes (H Joe et al.)
Optimal Truncation of Vines (D Kurowicka)
Bayesian Inference for D-Vines: Estimation and Model Selection (C Czado & A Min)
Analysis of Australian Electricity Loads Using Joint Bayesian Inference of D-Vines with Autoregressive Margins (C Czado et al.)
Non-Parametric Bayesian Belief Nets versus Vines (A Hanea)
Modeling Dependence Between Financial Returns Using Pair-Copula Constructions (K Aas & D Berg)
Dynamic D-Vine Model (A Heinen & A Valdesogo)
Summary and Future Directions (D Kurowicka)
Readership: Students, researchers and professionals in probability, statistics, finance and engineering.
“This book gives a clear and authoritative exposition of the vine methodology, which has recently emerged as a flexible tool for modeling high-dimensional data through pair-copula constructions. Leaders in the field join forces to provide a broad and insightful account of the existing theory as well as many new results of practical interest, from the enumeration and generation of regular vines to copula modeling and estimation using C-vines and D-vines. Many instructive illustrations and state-of-the-art applications are also presented, in static and dynamic contexts. Short of being ‘D-vine’, this important volume ought to become a classic of the copula literature and a useful reference for developers and practitioners alike!”
Christian Genest
Professor of Statistics
McGill University, Montréal, Canada
“Dependence modeling beyond linear correlation has become a key theme of research, with considerable promise in numerous applications. Especially the field of hierarchical model building has gained a lot of interest in this context. The notion of vine combines graphic with analytic tools from the realm of copulas, and offers a computationally as well as structurally interesting environment for the construction of multivariate models. Written by experts in the field, this handbook will be a most useful addition to a fast growing field of research in probability and statistics.”
Paul Embrechts
Director of RiskLab
ETH Zurich
“In this well-written and comprehensive book, an international team of more than one dozen researchers presents a thorough introduction to dependence modeling using vine copulas. The book assembles material formerly only available in journal articles and conference proceedings in a coherent and very readable manner. In 17 chapters, the authors present the basic and advanced vine copula properties and techniques for researchers wishing to employ this methodology in practice. The book has numerous examples, illustrations, algorithms, references, and directions for future work, and promises to be an important reference for years to come.”
Roger B Nelsen
Professor Emeritus
Lewis & Clark College
Dependence Modeling with Vine Copula 2011.pdf
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