Tail dependence of skew <i>t</i>-copulas

Kollo, Tõnu; Pettere, Gaida; Valge, Marju

doi:10.1080/03610918.2014.988979

Cited by 12 publications

(4 citation statements)

References 10 publications

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“…Gaussian. Such mixtures have the very convenient property of a known asymptotic behaviour: whilst mixtures of Gaussians and skew-normals have asymptotically independent extremes, Ts and skew-Ts exhibit extreme dependence (Kollo et al 2017). We discuss below in our simulation study that mixtures combining different elliptical structures did not provide any additional information about the extreme structure.…”

Section: Likelihoodmentioning

confidence: 94%

Semiparametric bivariate modelling with flexible extremal dependence

Leonelli

Friel

2019

Stat Comput

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Inference over multivariate tails often requires a number of assumptions which may affect the assessment of the extreme dependence structure. Models are usually constructed in such a way that extreme components can either be asymptotically dependent or be independent of each other. Recently, there has been an increasing interest on modelling multivariate extremes more flexibly, by allowing models to bridge both asymptotic dependence regimes. Here we propose a novel semiparametric approach which allows for a variety of dependence patterns, be them extremal or not, by using in a model-based fashion the full dataset. We build on previous work for inference on marginal exceedances over a high, unknown threshold, by combining it with flexible, semiparametric copula specifications to investigate extreme dependence, thus separately modelling marginals and dependence structure. Because of the generality of our approach, bivariate problems are investigated here due to computational challenges, but multivariate extensions are readily available. Empirical results suggest that our approach can provide sound uncertainty statements about the possibility of asymptotic independence, and we propose a criterion to quantify the presence of either extreme regime which performs well in our applications when compared to others available. Estimation of functions of interest for extremes is performed via MCMC algorithms. Attention is also devoted to the prediction of new extreme observations. Our approach is evaluated through simulations, applied to real data and assessed against competing approaches. Evidence demonstrates that the bulk of the data do not bias and improve the inferential process for extremal dependence in our applications.

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Section: Likelihoodmentioning

confidence: 94%

Semiparametric bivariate modelling with flexible extremal dependence

Leonelli

Friel

2019

Stat Comput

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“…Bortot [2] has studied tail dependence of the bivariate skew normal and skew t-distributions and derived inequalities for the tail dependence coefficients of these copulas. In more details tail behavior of the skew t-copula has been examined by simulation in Kollo et al [19]. Because of interest to multivariate distributions and corresponding to them copulas in applications a question about tail dependence for multivariate distributions has raised.…”

Section: Tail Dependence Coefficientsmentioning

confidence: 99%

Behaviour of multivariate tail dependence coefficients

Pettere

Voronova

Zariņa

2019

ACUTM

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In applications tail dependence is an important property of a copula. Bivariate tail dependence is investigated in many papers, but multivariate tail dependence has not been studied widely. We define multivariate upper and lower tail dependence coefficients as limits of the probability that values of one marginal will be large if at least one of other marginals will be as large also. Further we derive some relations between introduced tail dependence and bivariate tail dependence coefficients. Applications have shown that the multivariate t-copula has been successfully used in practice because of its tail dependence property. Therefore, t-copula can be used as an alternative method for risk assessment under Solvency II for insurance models. We have paid attention to the properties of the introduced multivariate tail dependence coefficient for t-copula and examine it in the simulation experiment.

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“…Tail dependence of multivariate tand skew t-distributions has been intensively studied in recent years, see Fung and Seneta [15] or Joe and Li [16], for example. In Kollo et al [17] it is shown that the upper tail dependence coefficient of the skew t-distribution can be several times bigger than the corresponding value of multivariate t-distribution. Moments and inferential aspects related to the multivariate skew t-distribution have been also actively studied in Padoan [18], Galarza et al [19], Zhou and He [20], Lee and McLachlan [5], DiCiccio and Monti [21], for instance.…”

Section: Introductionmentioning

confidence: 97%

Multivariate Skew t-Distribution: Asymptotics for Parameter Estimators and Extension to Skew t-Copula

2021

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Symmetric elliptical distributions have been intensively used in data modeling and robustness studies. The area of applications was considerably widened after transforming elliptical distributions into the skew elliptical ones that preserve several good properties of the corresponding symmetric distributions and increase possibilities of data modeling. We consider three-parameter p-variate skew t-distribution where p-vector μ is the location parameter, Σ:p×p is the positive definite scale parameter, p-vector α is the skewness or shape parameter, and the number of degrees of freedom ν is fixed. Special attention is paid to the two-parameter distribution when μ=0 that is useful for construction of the skew t-copula. Expressions of the parameters are presented through the moments and parameter estimates are found by the method of moments. Asymptotic normality is established for the estimators of Σ and α. Convergence to the asymptotic distributions is examined in simulation experiments.

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Tail dependence of skew t-copulas

Cited by 12 publications

References 10 publications

Semiparametric bivariate modelling with flexible extremal dependence

Semiparametric bivariate modelling with flexible extremal dependence

Behaviour of multivariate tail dependence coefficients

Multivariate Skew t-Distribution: Asymptotics for Parameter Estimators and Extension to Skew t-Copula

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