[PDF] Copula Modeling eBook

Author : Marius Hofert
Publisher : Springer
Page : 267 pages
File Size : 24,91 MB
Release : 2019-01-09
Category : Business & Economics
ISBN : 3319896350

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This book introduces the main theoretical findings related to copulas and shows how statistical modeling of multivariate continuous distributions using copulas can be carried out in the R statistical environment with the package copula (among others). Copulas are multivariate distribution functions with standard uniform univariate margins. They are increasingly applied to modeling dependence among random variables in fields such as risk management, actuarial science, insurance, finance, engineering, hydrology, climatology, and meteorology, to name a few. In the spirit of the Use R! series, each chapter combines key theoretical definitions or results with illustrations in R. Aimed at statisticians, actuaries, risk managers, engineers and environmental scientists wanting to learn about the theory and practice of copula modeling using R without an overwhelming amount of mathematics, the book can also be used for teaching a course on copula modeling.

Author : Marius Hofert
Publisher : Springer
Page : 267 pages
File Size : 27,41 MB
Release : 2019-01-18
Category : Business & Economics
ISBN : 9783319896342

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This book introduces the main theoretical findings related to copulas and shows how statistical modeling of multivariate continuous distributions using copulas can be carried out in the R statistical environment with the package copula (among others). Copulas are multivariate distribution functions with standard uniform univariate margins. They are increasingly applied to modeling dependence among random variables in fields such as risk management, actuarial science, insurance, finance, engineering, hydrology, climatology, and meteorology, to name a few. In the spirit of the Use R! series, each chapter combines key theoretical definitions or results with illustrations in R. Aimed at statisticians, actuaries, risk managers, engineers and environmental scientists wanting to learn about the theory and practice of copula modeling using R without an overwhelming amount of mathematics, the book can also be used for teaching a course on copula modeling.

Author : Pravin K. Trivedi
Publisher : Now Publishers Inc
Page : 126 pages
File Size : 26,68 MB
Release : 2007
Category : Business & Economics
ISBN : 1601980205

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Copula Modeling explores the copula approach for econometrics modeling of joint parametric distributions. Copula Modeling demonstrates that practical implementation and estimation is relatively straightforward despite the complexity of its theoretical foundations. An attractive feature of parametrically specific copulas is that estimation and inference are based on standard maximum likelihood procedures. Thus, copulas can be estimated using desktop econometric software. This offers a substantial advantage of copulas over recently proposed simulation-based approaches to joint modeling. Copulas are useful in a variety of modeling situations including financial markets, actuarial science, and microeconometrics modeling. Copula Modeling provides practitioners and scholars with a useful guide to copula modeling with a focus on estimation and misspecification. The authors cover important theoretical foundations. Throughout, the authors use Monte Carlo experiments and simulations to demonstrate copula properties

Author : Harry Joe
Publisher : World Scientific
Page : 370 pages
File Size : 14,21 MB
Release : 2011
Category : Business & Economics
ISBN : 981429988X

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1. Introduction : Dependence modeling / D. Kurowicka -- 2. Multivariate copulae / M. Fischer -- 3. Vines arise / R.M. Cooke, H. Joe and K. Aas -- 4. Sampling count variables with specified Pearson correlation : A comparison between a naive and a C-vine sampling approach / V. Erhardt and C. Czado -- 5. Micro correlations and tail dependence / R.M. Cooke, C. Kousky and H. Joe -- 6. The Copula information criterion and Its implications for the maximum pseudo-likelihood estimator / S. Gronneberg -- 7. Dependence comparisons of vine copulae with four or more variables / H. Joe -- 8. Tail dependence in vine copulae / H. Joe -- 9. Counting vines / O. Morales-Napoles -- 10. Regular vines : Generation algorithm and number of equivalence classes / H. Joe, R.M. Cooke and D. Kurowicka -- 11. Optimal truncation of vines / D. Kurowicka -- 12. Bayesian inference for D-vines : Estimation and model selection / C. Czado and A. Min -- 13. Analysis of Australian electricity loads using joint Bayesian inference of D-vines with autoregressive margins / C. Czado, F. Gartner and A. Min -- 14. Non-parametric Bayesian belief nets versus vines / A. Hanea -- 15. Modeling dependence between financial returns using pair-copula constructions / K. Aas and D. Berg -- 16. Dynamic D-vine model / A. Heinen and A. Valdesogo -- 17. Summary and future directions / D. Kurowicka

Author : Roger B. Nelsen
Publisher : Springer Science & Business Media
Page : 227 pages
File Size : 33,45 MB
Release : 2013-03-09
Category : Mathematics
ISBN : 1475730764

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Copulas are functions that join multivariate distribution functions to their one-dimensional margins. The study of copulas and their role in statistics is a new but vigorously growing field. In this book the student or practitioner of statistics and probability will find discussions of the fundamental properties of copulas and some of their primary applications. The applications include the study of dependence and measures of association, and the construction of families of bivariate distributions. With nearly a hundred examples and over 150 exercises, this book is suitable as a text or for self-study. The only prerequisite is an upper level undergraduate course in probability and mathematical statistics, although some familiarity with nonparametric statistics would be useful. Knowledge of measure-theoretic probability is not required. Roger B. Nelsen is Professor of Mathematics at Lewis & Clark College in Portland, Oregon. He is also the author of "Proofs Without Words: Exercises in Visual Thinking," published by the Mathematical Association of America.

Author : Harry Joe
Publisher : CRC Press
Page : 479 pages
File Size : 19,89 MB
Release : 2014-06-26
Category : Mathematics
ISBN : 1466583231

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Dependence Modeling with Copulas covers the substantial advances that have taken place in the field during the last 15 years, including vine copula modeling of high-dimensional data. Vine copula models are constructed from a sequence of bivariate copulas. The book develops generalizations of vine copula models, including common and structured facto

Author : Harry Joe
Publisher : CRC Press
Page : 483 pages
File Size : 35,53 MB
Release : 2014-06-26
Category : Mathematics
ISBN : 1466583223

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Dependence Modeling with Copulas covers the substantial advances that have taken place in the field during the last 15 years, including vine copula modeling of high-dimensional data. Vine copula models are constructed from a sequence of bivariate copulas. The book develops generalizations of vine copula models, including common and structured factor models that extend from the Gaussian assumption to copulas. It also discusses other multivariate constructions and parametric copula families that have different tail properties and presents extensive material on dependence and tail properties to assist in copula model selection. The author shows how numerical methods and algorithms for inference and simulation are important in high-dimensional copula applications. He presents the algorithms as pseudocode, illustrating their implementation for high-dimensional copula models. He also incorporates results to determine dependence and tail properties of multivariate distributions for future constructions of copula models.

Author : Fabrizio Durante
Publisher : CRC Press
Page : 331 pages
File Size : 16,50 MB
Release : 2015-07-01
Category : Mathematics
ISBN : 1439884447

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This book gives readers the solid and formal mathematical background to apply copulas to a range of mathematical areas, such as probability, real analysis, measure theory, and algebraic structures. The authors prove the results as simply as possible and unify various methods scattered throughout the literature in common frameworks, including shuffles of copulas. They also explore connections with related functions, such as quasi-copulas, semi-copulas, and triangular norms, that have been used in different domains.

Author : Li-Hsien Sun
Publisher : Springer Nature
Page : 141 pages
File Size : 47,76 MB
Release : 2020-07-01
Category : Business & Economics
ISBN : 9811549982

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This book provides statistical methodologies for time series data, focusing on copula-based Markov chain models for serially correlated time series. It also includes data examples from economics, engineering, finance, sport and other disciplines to illustrate the methods presented. An accessible textbook for students in the fields of economics, management, mathematics, statistics, and related fields wanting to gain insights into the statistical analysis of time series data using copulas, the book also features stand-alone chapters to appeal to researchers. As the subtitle suggests, the book highlights parametric models based on normal distribution, t-distribution, normal mixture distribution, Poisson distribution, and others. Presenting likelihood-based methods as the main statistical tools for fitting the models, the book details the development of computing techniques to find the maximum likelihood estimator. It also addresses statistical process control, as well as Bayesian and regression methods. Lastly, to help readers analyze their data, it provides computer codes (R codes) for most of the statistical methods.

Author : Piotr Jaworski
Publisher : Springer Science & Business Media
Page : 338 pages
File Size : 35,30 MB
Release : 2010-07-16
Category : Mathematics
ISBN : 3642124658

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Copulas are mathematical objects that fully capture the dependence structure among random variables and hence offer great flexibility in building multivariate stochastic models. Since their introduction in the early 50's, copulas have gained considerable popularity in several fields of applied mathematics, such as finance, insurance and reliability theory. Today, they represent a well-recognized tool for market and credit models, aggregation of risks, portfolio selection, etc. This book is divided into two main parts: Part I - "Surveys" contains 11 chapters that provide an up-to-date account of essential aspects of copula models. Part II - "Contributions" collects the extended versions of 6 talks selected from papers presented at the workshop in Warsaw.