Book contents
- Copulas and Their Applications in Water Resources Engineering
- Copulas and Their Applications in Water Resources Engineering
- Copyright page
- Dedication
- Contents
- Preface
- Acknowledgments
- Part One Theory
- 1 Introduction
- 2 Preliminaries
- 3 Copulas and Their Properties
- 4 Symmetric Archimedean Copulas
- 5 Asymmetric Copulas
- 6 Plackett Copula
- 7 Non-Archimedean Copulas
- 8 Entropic Copulas
- 9 Copulas in Time Series Analysis
- Part Two Applications
- Index
- References
5 - Asymmetric Copulas
High Dimension
from Part One - Theory
Published online by Cambridge University Press: 03 January 2019
- Copulas and Their Applications in Water Resources Engineering
- Copulas and Their Applications in Water Resources Engineering
- Copyright page
- Dedication
- Contents
- Preface
- Acknowledgments
- Part One Theory
- 1 Introduction
- 2 Preliminaries
- 3 Copulas and Their Properties
- 4 Symmetric Archimedean Copulas
- 5 Asymmetric Copulas
- 6 Plackett Copula
- 7 Non-Archimedean Copulas
- 8 Entropic Copulas
- 9 Copulas in Time Series Analysis
- Part Two Applications
- Index
- References
Summary
Much of the literature on copulas, discussed in the previous chapters, is limited to the bivariate cases. The Gaussian and student copulas have been commonly applied to model the dependence in higher dimensions (Genest and Favre, 2007; Genest et al., 2007a). In Chapter 4, we discussed the extension of symmetric bivariate Archimedean copulas as well as their major restrictions to model high-dimensional dependence (i.e., d ≥ 3)d≥3). Through the extension of the bivariate Archimedean copula, the multivariate Archimedean copula is symmetric and denoted as exchangeable Archimedean copula (EAC). EAC allows for the specification of only one generating function and only one set of parameters θ. In other words, random variates by pair share the same degree of dependence. Using the trivariate random variable {X1, X2, X3} as an example, {X1, X2}, {X2, X3}, and {X1, X3} should have the same degree of dependence. However, this assumption is rarely valid. This chapter discusses the following two approaches of constructing asymmetric multivariate copulas: nested Archimedean copula construction (NAC) and the vine copulas through pair-copula construction (PCC).
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- Copulas and their Applications in Water Resources Engineering , pp. 172 - 241Publisher: Cambridge University PressPrint publication year: 2019