Tail dependence for two skew distributions

Fung, Thomas; Seneta, E.

doi:10.1016/j.spl.2010.01.011

Cited by 33 publications

(25 citation statements)

References 13 publications

(16 reference statements)

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“…In contrast to skew-normal distributions, skewness parameters affect tail dependence parameters significantly for the multivariate t distributions due to slower heavy tail decays. To illustrate this and also the fact that our results match the results reported in [10,22], we consider the calculations of bivariate tail dependence parameters. For a bivariate skew-t density with δ 1 , δ 2 that are compatible with ρ,…”

Section: Tail Densities Of Skew-t Distributionssupporting

confidence: 70%

Tail densities of skew-elliptical distributions

Joe

2019

Journal of Multivariate Analysis

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Skew-elliptical distributions constitute a large class of multivariate distributions that account for both skewness and a variety of tail properties. This class has simpler representations in terms of densities rather than cumulative distribution functions, and the tail density approach has previously been developed to study tail properties when multivariate densities have more tractable forms. The special skew-elliptical structure allows for derivations of specific forms for the tail densities for those skew-elliptical copulas that admit probability density functions, under heavy and light tail conditions on density generators. The tail densities of skew-elliptical copulas are explicit and depend only on tail properties of the underlying density generator and conditions on the skewness parameters. In the heavy tail case skewness parameters affect tail densities of the skew-elliptical copulas more profoundly than that in the light tail case, whereas in the latter case the tail densities of skew-elliptical copulas are only proportional to the tail densities of symmetrical elliptical copulas. Various examples, including tail densities of skew-normal and skew-t distributions, are given.

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Section: Tail Densities Of Skew-t Distributionssupporting

confidence: 70%

Tail densities of skew-elliptical distributions

Joe

2019

Journal of Multivariate Analysis

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“…This skew t distribution possesses nontrivial values of tail dependence under all conditions. The proof of this result can be found in Fung and Seneta [7]. However, it should also be noted that positivity of λ L , as defined in (3) is too extreme a measure as discussed in Fung and Seneta [8], since under independence of marginals, the numerator in (6) is u 2 and the limit λ in (3) is zero.…”

Section: Theoremmentioning

confidence: 77%

Rate of Decay of the Tail Dependence Coefficient for the Skew t Distribution

Fung

2012

Sri Lankan J App Stats

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We examine the rate of decay to zero of the tail dependence coefficient of the bivariate skew t distribution which is obtained via normal variance-mean mixture in a case where there is no asymptotic tail dependence. Our result helps to explain the difference in performance in model fitting between this skew t distribution and the one based on the variance mixing of the bivariate skew-normal distribution. This t distribution always displays asymptotic tail dependence, as happens in the symmetric case which is common to both models.

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“…We summarize the results in the following theorem. The proof of the theorem can be found in Fung & Seneta (2010b). THEOREM 3.…”

Section: Tail Dependencementioning

confidence: 99%

Modelling and Estimation for Bivariate Financial Returns

Fung

Seneta

2010

Int Statistical Rev

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Maximum likelihood estimates are obtained for long data sets of bivariate financial returns using mixing representation of the bivariate (skew) Variance Gamma (VG) and two (skew) "t" distributions. By analysing simulated and real data, issues such as asymptotic lower tail dependence and competitiveness of the three models are illustrated. A brief review of the properties of the models is included. The present paper is a companion to papers in this journal by Demarta & McNeil and Finlay & Seneta. Copyright (c) 2010 The Authors. Journal compilation (c) 2010 International Statistical Institute.

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Tail dependence for two skew distributions

Cited by 33 publications

References 13 publications

Tail densities of skew-elliptical distributions

Tail densities of skew-elliptical distributions

Rate of Decay of the Tail Dependence Coefficient for the Skew t Distribution

Modelling and Estimation for Bivariate Financial Returns

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