Nested Archimedean Copulas Meet R: The nacopula Package

The package nacopula provides procedures for constructing nested Archimedean copulas in any dimensions and with any kind of nesting structure, generating vectors of random variates from the constructed objects, computing function values and probabilities of falling into hypercubes, as well as evaluation of characteristics such as Kendall's tau and the tail-dependence coefficients. As by-products, algorithms for various distributions, including exponentially tilted stable and Sibuya distributions, are implemented. Detailed examples are given.

Extreme-Value Copulas

Being the limits of copulas of componentwise maxima in independent random samples, extreme-value copulas can be considered to provide appropriate models for the dependence structure between rare events. Extreme-value copulas not only arise naturally in the domain of extreme-value theory, they can also be a convenient choice to model general positive dependence structures. The aim of this survey is to present the reader with the state-of-the-art in dependence modeling via extreme-value copulas. Both probabilistic and statistical issues are reviewed, in a nonparametric as well as a parametric context.Comment: 20 pages, 3 figures. Minor revision, typos corrected. To appear in F. Durante, W. Haerdle, P. Jaworski, and T. Rychlik (editors) "Workshop on Copula Theory and its Applications", Lecture Notes in Statistics -- Proceedings, Springer 201

Methods of Tail Dependence Estimation

Characterization and quantification of climate extremes and their dependencies are fundamental to the studying of natural hazards. This chapter reviews various parametric and nonparametric tail dependence coefficient estimators. The tail dependence coefficient describes the dependence (degree of association) between concurrent extremes at different locations. Accurate and reliable knowledge of the spatial characteristics of extremes can help improve the existing methods of modeling the occurrence probabilities of extreme events. This chapter will review these methods and use two case studies to demonstrate the application of tail dependence analysis

Nonparametric estimation of the tail-dependence coefficient

A common measure of tail dependence is the so-called tail-dependence coefficient. We present a nonparametric estimator of the tail-dependence coefficient and prove its strong consistency and asymptotic normality in the case of known marginal distribution functions. The finite-sample behavior as well as robustness will be assessed through simulation. Although it has a good performance, it is sensitive to the extreme value dependence assumption. We shall see that a block maxima procedure might improve the estimation. This will be illustrated through simulation. An application to financial data shall be presented at the end.Este trabalho é financiado por Fundos FEDER através do Programa Operacional Factores de Competitividade - COMPETE e por Fundos Nacionais através da FCT - Fundação para a Ciência e a Tecnologia no âmbito do projecto PEst-C/MAT/UI0013/2011