Related papers: Operator Tail Dependence of Copulas

For extreme value copulas with a known upper tail dependence coefficient we find pointwise upper and lower bounds, which are used to establish upper and lower bounds of the Spearman and Kendall correlation coefficients. We shown that in all…

In this paper, we study dependence uncertainty and the resulting effects on tail risk measures, which play a fundamental role in modern risk management. We introduce the notion of a regular dependence measure, defined on multi-marginal…

Multivariate time series exhibit two types of dependence: across variables and across time points. Vine copulas are graphical models for the dependence and can conveniently capture both types of dependence in the same model. We derive the…

Copula models are flexible tools to represent complex structures of dependence for multivariate random variables. According to Sklar's theorem (Sklar, 1959), any d-dimensional absolutely continuous density can be uniquely represented as the…

Data exhibiting heavy-tails in one or more dimensions is often studied using the framework of regular variation. In a multivariate setting this requires identifying specific forms of dependence in the data; this means identifying that the…

Regular variation is often used as the starting point for modeling multivariate heavy-tailed data. A random vector is regularly varying if and only if its radial part $R$ is regularly varying and is asymptotically independent of the angular…

We review ideas on temporal dependences and recurrences in discrete time series from several areas of natural and social sciences. We revisit existing studies and redefine the relevant observables in the language of copulas (joint laws of…

This paper introduces vector copulas associated with multivariate distributions with given multivariate marginals, based on the theory of measure transportation, and establishes a vector version of Sklar's theorem. The latter provides a…

We propose an instrumental variable framework for identifying and estimating causal effects of discrete and continuous treatments with binary instruments. The basis of our approach is a local copula representation of the joint distribution…

Copulas have been popular to model dependence for multivariate distributions, but have not been used much in modelling temporal dependence of univariate time series. This paper demonstrates some difficulties with using copulas even for…

A bivariate random vector can exhibit either asymptotic independence or dependence between the largest values of its components. When used as a statistical model for risk assessment in fields such as finance, insurance or meteorology, it is…

So far, one-factor copulas induce conditional independence with respect to a latent factor. In this paper, we extend one-factor copulas to conditionally dependent models. This is achieved through new representations which allow to build new…

We study a broad class of asymmetric copulas introduced by Liebscher (2008) as a combination of multiple - usually symmetric - copulas. The main thrust of the paper is to provide new theoretical properties including exact tail dependence…

In risk management, tail risks are of crucial importance. The assessment of risks should be carried out in accordance with the regulatory authority's requirement at high quantiles. In general, the underlying distribution function is…

Motivated by recently investigated results on dependence measures and robust risk models, this paper provides an overview of dependence properties of many well-known bivariate copula families, where the focus is on the Schur order for…

We formulate a uniform tail bound for empirical processes indexed by a class of functions, in terms of the individual deviations of the functions rather than the worst-case deviation in the considered class. The tail bound is established by…

We propose a mean functional which exists for any probability distributions, and which characterizes the Pareto distribution within the set of distributions with finite left endpoint. This is in sharp contrast to the mean excess plot which…

The multivariate version of the Mixed Tempered Stable is proposed. It is a generalization of the Normal Variance Mean Mixtures. Characteristics of this new distribution and its capacity in fitting tails and capturing dependence structure…

We present a new family of estimators of the Weibull tail-coefficient. The Weibull tail-coefficient is defined as the regular variation coefficient of the inverse failure rate function. Our estimators are based on a linear combination of…

In some fields of applications of stable distributions, especially in economics, it appears, that data have distributions similar to stable in a large region, but do not have such heavy tails. Our aim in this note is to propose several…