Displaying similar documents to “Multivariate measures of concordance for copulas and their marginals”

Copula–Induced Measures of Concordance

Sebastian Fuchs (2016)

Dependence Modeling

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We study measures of concordance for multivariate copulas and copulas that induce measures of concordance. To this end, for a copula A, we consider the maps C → R given by [...] where C denotes the collection of all d–dimensional copulas, M is the Fréchet–Hoeffding upper bound, Π is the product copula, [. , .] : C × C → R is the biconvex form given by [C, D] := ∫ [0,1]d C(u) dQD(u) with the probability measure QD associated with the copula D, and ψΛ C → C is a transformation of copulas....

A Biconvex Form for Copulas

Sebastian Fuchs (2016)

Dependence Modeling

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We study the integration of a copula with respect to the probability measure generated by another copula. To this end, we consider the map [. , .] : C × C → R given by [...] where C denotes the collection of all d–dimensional copulas and QD denotes the probability measures associated with the copula D. Specifically, this is of interest since several measures of concordance such as Kendall’s tau, Spearman’s rho and Gini’s gamma can be expressed in terms of the map [. , .]. Quite generally,...

Multivariate extensions of expectiles risk measures

Véronique Maume-Deschamps, Didier Rullière, Khalil Said (2017)

Dependence Modeling

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This paper is devoted to the introduction and study of a new family of multivariate elicitable risk measures. We call the obtained vector-valued measures multivariate expectiles. We present the different approaches used to construct our measures. We discuss the coherence properties of these multivariate expectiles. Furthermore, we propose a stochastic approximation tool of these risk measures.

Bounds on integrals with respect to multivariate copulas

Michael Preischl (2016)

Dependence Modeling

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In this paper, we present a method to obtain upper and lower bounds on integrals with respect to copulas by solving the corresponding assignment problems (AP’s). In their 2014 paper, Hofer and Iacó proposed this approach for two dimensions and stated the generalization to arbitrary dimensons as an open problem. We will clarify the connection between copulas and AP’s and thus find an extension to the multidimensional case. Furthermore, we provide convergence statements and, as applications,...

Bivariate copulas, norms and non-exchangeability

Pier Luigi Papini (2015)

Dependence Modeling

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The present paper is related to the study of asymmetry for copulas by introducing functionals based on different norms for continuous variables. In particular, we discuss some facts concerning asymmetry and we point out some flaws occurring in the recent literature dealing with this matter.

On uniform tail expansions of multivariate copulas and wide convergence of measures

Piotr Jaworski (2006)

Applicationes Mathematicae

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The theory of copulas provides a useful tool for modeling dependence in risk management. In insurance and finance, as well as in other applications, dependence of extreme events is particularly important, hence there is a need for a detailed study of the tail behaviour of multivariate copulas. We investigate the class of copulas having regular tails with a uniform expansion. We present several equivalent characterizations of uniform tail expansions. Next, basing on them, we determine...

Forecasting time series with multivariate copulas

Clarence Simard, Bruno Rémillard (2015)

Dependence Modeling

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In this paper we present a forecasting method for time series using copula-based models for multivariate time series. We study how the performance of the predictions evolves when changing the strength of the different possible dependencies, as well as the structure of the dependence. We also look at the impact of the marginal distributions. The impact of estimation errors on the performance of the predictions is also considered. In all the experiments, we compare predictions from our...

Constructing copulas by means of pairs of order statistics

Ali Dolati, Manuel Úbeda-Flores (2009)

Kybernetika

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In this paper, we introduce two transformations on a given copula to construct new and recover already-existent families. The method is based on the choice of pairs of order statistics of the marginal distributions. Properties of such transformations and their effects on the dependence and symmetry structure of a copula are studied.

My introduction to copulas

Fabrizio Durante, Giovanni Puccetti, Matthias Scherer, Steven Vanduffel (2017)

Dependence Modeling

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