Topic
Vine copula
About: Vine copula is a research topic. Over the lifetime, 654 publications have been published within this topic receiving 26126 citations.
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01 Jan 1999
TL;DR: This book discusses the fundamental properties of copulas and some of their primary applications, which include the study of dependence and measures of association, and the construction of families of bivariate distributions.
Abstract: 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. This book is suitable as a text or for self-study.
8,626 citations
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TL;DR: This work uses the pair-copula decomposition of a general multivariate distribution and proposes a method for performing inference, which represents the first step towards the development of an unsupervised algorithm that explores the space of possible pair-Copula models, that also can be applied to huge data sets automatically.
Abstract: Building on the work of Bedford, Cooke and Joe, we show how multivariate data, which exhibit complex patterns of dependence in the tails, can be modelled using a cascade of pair-copulae, acting on two variables at a time. We use the pair-copula decomposition of a general multivariate distribution and propose a method for performing inference. The model construction is hierarchical in nature, the various levels corresponding to the incorporation of more variables in the conditioning sets, using pair-copulae as simple building blocks. Pair-copula decomposed models also represent a very flexible way to construct higher-dimensional copulae. We apply the methodology to a financial data set. Our approach represents the first step towards the development of an unsupervised algorithm that explores the space of possible pair-copula models, that also can be applied to huge data sets automatically.
1,744 citations
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TL;DR: In this paper, the authors test for asymmetry in a model of the dependence between the Deutsche mark and the yen, in the sense that a different degree of correlation is exhibited during joint appreciations against the U.S. dollar versus during joint depreciations.
Abstract: We test for asymmetry in a model of the dependence between the Deutsche mark and the yen, in the sense that a different degree of correlation is exhibited during joint appreciations against the U.S. dollar versus during joint depreciations. We consider an extension of the theory of copulas to allow for conditioning variables, and employ it to construct flexible models of the conditional dependence structure of these exchange rates. We find evidence that the mark‐dollar and yen‐dollar exchange rates are more correlated when they are depreciating against the dollar than when they are appreciating.
1,666 citations
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TL;DR: This paper presents an introduction to inference for copula models, based on rank methods, by working out in detail a small, fictitious numerical example, the various steps involved in investigating the dependence between two random variables and in modeling it using copulas.
Abstract: This paper presents an introduction to inference for copula models, based on rank methods. By working out in detail a small, fictitious numerical example, the writers exhibit the various steps involved in investigating the dependence between two random variables and in modeling it using copulas. Simple graphical tools and numerical techniques are presented for selecting an appropriate model, estimating its parameters, and checking its goodness-of-fit. A larger, realistic application of the methodology to hydrological data is then presented.
1,414 citations
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TL;DR: A new graphical model, called a vine, for dependent random variables, which generalize the Markov trees often used in modelling high-dimensional distributions and is weakened to allow for various forms of conditional dependence.
Abstract: A new graphical model, called a vine, for dependent random variables is introduced. Vines generalize the Markov trees often used in modelling high-dimensional distributions. They differ from Markov trees and Bayesian belief nets in that the concept of conditional independence is weakened to allow for various forms of conditional dependence.
1,247 citations