Tail dependence functions and vine copulas

By Harry Joe, Haijun Li, Aristidis K. Nikoloulopoulos. Journal of Multivariate Analysis, 2010

327 citations recorded by the source corpus.

Tail dependence and conditional tail dependence functions describe, respectively, the tail probabilities and conditional tail probabilities of a copula at various relative scales. The properties as well as the interplay of these two functions are established based upon their homogeneous structures. The extremal dependence of a copula, as described by its extreme value copulas, is shown to be completely determined by its tail dependence functions. For a vine copula built from a set of bivariate copulas, its tail dependence function can be expressed recursively by the tail dependence and conditional tail dependence functions of lower-dimensional margins. The effect of tail dependence of bivariate linking copulas on that of a vine copula is also investigated.

Subfields: Economics and Econometrics, Finance

View Paper: https://www.semanticscholar.org/paper/e8f6a1f33bcd8f75ea1860856019e00ac070ba14

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Citations in the corpus

Asymptotic Analysis of Multivariate Tail Conditional Expectations (2012, methodology): “A multivariate regular variation method based on the tail dependence function (see Joe et al. 2010; Li and Sun 2009) was developed in Joe and Li (2011) to derive tractable asymptotic bounds for multivariate TCEs, but these bounds are expressed in terms of univariate integrals of tail dependence…”
Pair Copula Constructions for Multivariate Discrete Data (2012, background): “( 2010 ) for a detailed discussion), the bivariate version is more commonly referred to as the Clayton copula.”
Selecting and estimating regular vine copulae and application to financial returns (2012, background): “While the Student-t copula allows for symmetric tail dependence as measured by the tail dependence coeﬃcient or tail dependence function (see for example Joe et al. (2010)) it has only a single parameter to control tail dependence of all pairs of variables.”
Modeling Dependence with C- and D-Vine Copulas: The R Package CDVine (2013, background): “…copulas obtained from C-and D-vine structures, so-called C-and D-vine copulas , constitute very ﬂexible models, since bivariate copulas can easily accommodate complex dependence structures such as asymmetric dependence or strong joint tail behavior (see Joe, Li, and Nikoloulopoulos 2010).”
Risk management with high-dimensional vine copulas: An analysis of the Euro Stoxx 50 (2013, background): “This is underlined by Joe et al. (2010) who show that in order for a vine copula to have (tail) dependence for all bivariate margins, it is sufficient for the bivariate copulas in the first tree to have (tail) dependence.”
Copula-Based Measures of Multivariate Association (2010, unknown): “[59], see also reference therein.”
Tail Dependence for Heavy-Tailed Scale Mixtures of Multivariate Distributions (2009, methodology): “It was shown in [12] that b∗(w; C) > 0 for all w ∈ R+ if and only if b∗(1, .”
Tail Risk of Multivariate Regular Variation (2011, methodology): “In fact, various upper tail dependence parameters can be represented by the upper tail dependence function [21, 29, 18], defined as follows,”
Parameter estimation for pair-copula constructions (2013, background): “ ground, and increases by one for each level, to ensure coherence of the construction. Despite its simple structure, the PCC is highly ﬂexible and coversa wide rangeofcomplex dependencies (Joe et al. [25], Hobæk Haﬀ et al. [21]). After Aas et al. [1] set it in an inferential context, it has made sev”