Some Results on Weak and Strong Tail Dependence Coefficients for Means of Copulas

نویسندگان

  • Matthias Fischer
  • Ingo Klein
چکیده

Copulas represent the dependence structure of multivariate distributions in a natural way. In order to generate new copulas from given ones, several proposals found its way into statistical literature. One simple approach is to consider convex-combinations (i.e. weighted arithmetic means) of two or more copulas. Similarly, one might consider weighted geometric means. Consider, for instance, the Spearman copula, defined as the geometric mean of the maximum and the independence copula. In general, it is not known whether weighted geometric means of copulas produce copulas, again. However, applying a recent result of Liebscher (2006), we show that every weighted geometric mean of extreme-value copulas produces again an extreme-value copula. The second contribution of this paper is to calculate extremal dependence measures (e.g. weak and strong tail dependence coefficients) for (weighted) geometric and arithmetic means of two copulas.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Tail dependence for weighted mean of two copula function

In this paper, we study the properties of power weighted means, arithmetic, geometry and harmonic for two copulas.

متن کامل

On tail dependence coefficients of transformed multivariate Archimedean copulas

This paper presents the impact of a class of transformations of copulas in their upper and lower multivariate tail dependence coefficients. In particular we focus on multivariate Archimedean copulas. In the first part of this paper, we calculate multivariate tail dependence coefficients when the generator of the considered copula exhibits some regular variation properties, and we investigate th...

متن کامل

Limiting Dependence Structures for Tail Events, with Applications to Credit Derivatives

Dependence structures for bivariate extremal events are analyzed using particular types of copula. Weak convergence results for copulas along the lines of the Pickands–Balkema– de Haan theorem provide limiting dependence structures for bivariate tail events. A characterization of these limiting copulas is also provided by means of invariance properties. The results obtained are applied to the c...

متن کامل

General Multivariate Dependence Using Associated Copulas

This paper studies the general multivariate dependence of a random vector using associated copulas. We extend definitions and results of positive dependence to the general dependence case. This includes associated tail dependence functions and associated tail dependence coefficients. We derive the relationships among associated copulas and study the associated copulas of the perfect dependence ...

متن کامل

Intermediate Tail Dependence: A Review and Some New Results

The concept of intermediate tail dependence is useful if one wants to quantify the degree of positive dependence in the tails when there is no strong evidence of presence of the usual tail dependence. We first review existing studies on intermediate tail dependence, and then we report new results to supplement the review. Intermediate tail dependence for elliptical, extreme value and Archimedea...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2007