On the Copula for Multivariate Extreme Value Distributions
نویسندگان
چکیده
We show that all multivariate Extreme Value distributions, which are the possible weak limits of the K largest order statistics of iid sequences, have the same copula, the so called K-extremal copula. This copula is described through exact expressions for its density and distribution functions. We also study measures of dependence, we obtain a weak convergence result and we propose a simulation algorithm for the K-extremal copula.
منابع مشابه
Measure of financial risk using conditional extreme value copulas with EVT margins
In this paper we propose a method to estimate the value-at-risk (VaR) of a portfolio based on a combination of time series, extreme value theory and copula fitting. Given multivariate financial data, we use a univariate ARMA-GARCH model for each return series. We then fit a generalized Pareto distribution to the tails of the residuals to model the distributions of marginal residuals, followed b...
متن کاملOrthant tail dependence of multivariate extreme value distributions
AMS 2000 subject classifications: 62H20 62P05 Keywords: Tail dependence Heavy tails Copula Multivariate extreme value distribution Marshall–Olkin distribution Archimedean copula Contagion risk a b s t r a c t The orthant tail dependence describes the relative deviation of upper-(or lower-) orthant tail probabilities of a random vector from similar orthant tail probabilities of a subset of its c...
متن کاملOn the bivariate Sarmanov distribution and copula. An application on insurance data using truncated marginal distributions
The Sarmanov family of distributions can provide a good model for bivariate random variables and it is used to model dependency in a multivariate setting with given marginals. In this paper, we focus our attention on the bivariate Sarmanov distribution and copula with different truncated extreme value marginal distributions. We compare a global estimation method based on maximizing the full log...
متن کاملSome Results on Weak and Strong Tail Dependence Coefficients for Means of Copulas
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...
متن کاملEstimating Risk of Natural Gas Portfolios by Using GARCH-EVT-Copula Model
This paper concentrates on estimating the risk of Title Transfer Facility (TTF) Hub natural gas portfolios by using the GARCH-EVT-copula model. We first use the univariate ARMA-GARCH model to model each natural gas return series. Second, the extreme value distribution (EVT) is fitted to the tails of the residuals to model marginal residual distributions. Third, multivariate Gaussian copula and ...
متن کامل