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1
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New copulas based on general partitions-of-unity and their applications to risk management

100%
Pfeifer D., Tsatedem H. A., Mändle A., Girschig C.
Dependence Modeling
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2016
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tom 4
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nr 1
EN
We construct new multivariate copulas on the basis of a generalized infinite partition-of-unity approach. This approach allows, in contrast to finite partition-of-unity copulas, for tail-dependence as well as for asymmetry. A possibility of fitting such copulas to real data from quantitative risk management is also pointed out.
2
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Copula–Induced Measures of Concordance

100%
Fuchs S.
Dependence Modeling
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2016
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tom 4
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nr 1
EN
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. We present conditions on ψΛ and on A under which these maps are measures of concordance. The resulting class of measures of concordance is rich and includes the well–known examples Spearman’s rho and Gini’s gamma.
3
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Joint weak hazard rate order under non-symmetric copulas

100%
Pellerey F., Spizzichino F.
Dependence Modeling
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2016
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tom 4
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nr 1
EN
A weak version of the joint hazard rate order, useful to stochastically compare not independent random variables, has been recently defined and studied in [4]. In the present paper, further results on this order are proved and discussed. In particular, some statements dealing with the relationships between the jointweak hazard rate order and other stochastic orders are generalized to the case of non symmetric copulas, and its relations with some multivariate aging notions (studied in [2]) are presented. For this purpose, the new notions of Generalized Supermigrative and Generalized Submigrative copulas are defined. Other new results, examples and discussions are provided as well.
4
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Baire category results for quasi–copulas

100%
Durante F., Fernández-Sánchez J., Trutschnig W.
Dependence Modeling
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2016
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tom 4
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nr 1
EN
The aim of this manuscript is to determine the relative size of several functions (copulas, quasi– copulas) that are commonly used in stochastic modeling. It is shown that the class of all quasi–copulas that are (locally) associated to a doubly stochastic signed measure is a set of first category in the class of all quasi– copulas. Moreover, it is proved that copulas are nowhere dense in the class of quasi-copulas. The results are obtained via a checkerboard approximation of quasi–copulas.
5
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An empirical almost sure central limit theorem under the weak dependence assumptions and its application to copula processes

100%
Dudziński M.
Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica
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2017
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tom 71
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nr 1
EN
Let: \(\mathbf{Y=}\left( \mathbf{Y}_{i}\right)\), where \(\mathbf{Y}_{i}=\left( Y_{i,1},...,Y_{i,d}\right)\), \(i=1,2,\dots \), be a \(d\)-dimensional, identically distributed, stationary, centered process with uniform marginals and a joint cdf \(F\), and \(F_{n}\left( \mathbf{x}\right) :=\frac{1}{n}\sum_{i=1}^{n}\mathbb{I}\left(Y_{i,1}\leq x_{1},\dots ,Y_{i,d}\leq x_{d}\right)\) denote the corresponding empirical cdf. In our work, we prove the almost sure central limit theorem for an empirical process \(B_{n}=\sqrt{n}\left( F_{n}-F\right)\) under some weak dependence conditions due to Doukhan and Louhichi. Some application of the established result to copula processes is also presented.
6
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New copulas based on general partitions-of-unity and their applications to risk management (part II)

100%
Pfeifer D., Mändle A., Ragulina O.
Dependence Modeling
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2017
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tom 5
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nr 1
246-255
EN
We present a constructive and self-contained approach to data driven infinite partition-of-unity copulas that were recently introduced in the literature. In particular, we consider negative binomial and Poisson copulas and present a solution to the problem of fitting such copulas to highly asymmetric data in arbitrary dimensions.
7
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A Biconvex Form for Copulas

88%
Fuchs S.
Dependence Modeling
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2016
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tom 4
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nr 1
EN
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, the map [. , .] can be applied to construct and investigate measures of concordance.
8
Content available remote

Dependence Measuring from Conditional Variances

88%
Kamnitui N., Santiwipanont T., Sumetkijakan S.
Dependence Modeling
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2015
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tom 3
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nr 1
EN
A conditional variance is an indicator of the level of independence between two random variables. We exploit this intuitive relationship and define a measure v which is almost a measure of mutual complete dependence. Unsurprisingly, the measure attains its minimum value for many pairs of non-independent ran- dom variables. Adjusting the measure so as to make it invariant under all Borel measurable injective trans- formations, we obtain a copula-based measure of dependence v* satisfying A. Rényi’s postulates. Finally, we observe that every nontrivial convex combination of v and v* is a measure of mutual complete dependence.
9
Content available remote

Dependence of Stock Returns in Bull and Bear Markets

63%
Dobric J., Frahm G., Schmid F.
Dependence Modeling
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2013
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tom 1
94-110
EN
Despite of its many shortcomings, Pearson’s rho is often used as an association measure for stock returns. A conditional version of Spearman’s rho is suggested as an alternative measure of association. This approach is purely nonparametric and avoids any kind of model misspecification. We derive hypothesis tests for the conditional rank-correlation coefficients particularly arising in bull and bear markets and study their finite-sample performance by Monte Carlo simulation. Further, the daily returns on stocks contained in the German stock index DAX 30 are analyzed. The empirical study reveals significant differences in the dependence of stock returns in bull and bear markets.
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