Construction of asymmetric multivariate copulas

By Eckhard Liebscher. 2008

241 citations recorded by the source corpus.

In this paper we introduce two methods for the construction of asymmetric multivariate copulas. The first is connected with products of copulas. The second approach generalises the Archimedean copulas. The resulting copulas are asymmetric and may have more than two parameters in contrast to most of the parametric families of copulas described in the literature. We study the properties of the proposed families of copulas such as the dependence of two components (Kendall's tau, tail dependence), marginal distributions and the generation of random variates.

Subfields: Demography, Finance, Global and Planetary Change

View Paper: https://www.semanticscholar.org/paper/8b4b42f020506cef977900f4702b025d0e645e7f

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Citations in the corpus

Copula-based geostatistical modeling of continuous and discrete data including covariates (2010, methodology): “Here we use a different construction principle for radially asymmetric copulas which was proved by Liebscher (2008) : Let C1; ... ; Ck : I n ! I be copulas and gji : I ! I”
Multivariate multiparameter extreme value models and return periods: A copula approach (2010, methodology): “The basic theoretical result is given by the following theorem, which represents a special case of a more general result stated by Liebscher [2008] .”
Large‐sample tests of extreme‐value dependence for multivariate copulas (2011, methodology): “, 2011, for a detailed discussion of this matter), only the Gumbel–Hougaard (GH) and its asymmetric version (aGH) defined using Khoudraji’s device (Khoudraji, 1995; Genest, Ghoudi, & Rivest, 1998; Liebscher, 2008) were used in the simulations.”
Mixed Cumulative Distribution Networks (2010, background): “where aS = {av}v∈S can be shown to be a copula itself (Liebscher, 2008).”
Copula Theory: An Introduction (2010, background): “To the best of our knowledgement, the idea of such constructions arose in the Khoudraji’s work [107], and, then, studied and further generalized in [23, 41, 79, 124].”
Analysis of directional dependence using asymmetric copula-based regression models (2014, background): “Liebscher [13] and Durante [14] introduced a general formula for new families of copulas whose members are asymmetric by multiplying two symmetric copulas: C(u, v; φ) = C1(uα , vβ) C2(uᾱ , vβ̄ ), (9) where α, β ∈ (0, 1), α = 1/2 or β = 1/2, α + ᾱ=1, β + β̄=1, and C1 and C2 are two symmetric copula”
A goodness-of-fit test for bivariate extreme-value copulas (2011, methodology): “These copulas were derived using Khoudraji’s device [15, 23, 28], which transforms any symmetric copula Cθ into a non-exchangeable model via the formula Cλ,κ,θ(u, v) = u vCθ(u , v)”