Multivariate Archimax copulas

Charpentier, Arthur; Fougères, Anne-Laure; Genest, Christian; Nešlehová, Johanna

doi:10.1016/j.jmva.2013.12.013

Cited by 57 publications

(80 citation statements)

References 19 publications

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“…The values are calculated based on 3000 Monte Carlo repetitions. Simulated samples from the Archimax copulas are generated by the algorithm described in Section 5.2 in Charpentier et al (2014). The results perfectly match the expected behavior: for model ψ 1 , the relative efficiencies are close to 1 (in fact, they are all slightly above 1), while they are decreasing for ψ 2 and increasing for ψ 3 .…”

Section: Consequences For Estimation Precisionmentioning

confidence: 52%

On second order conditions in the multivariate block maxima and peak over threshold method

Bücher

Volgushev

Zou

2019

Journal of Multivariate Analysis

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Second order conditions provide a natural framework for establishing asymptotic results about estimators for tail related quantities. Such conditions are typically tailored to the estimation principle at hand, and may be vastly different for estimators based on the block maxima (BM) method or the peak-over-threshold (POT) approach. In this paper we provide details on the relationship between typical second order conditions for BM and POT methods in the multivariate case. We show that the two conditions typically imply each other, but with a possibly different second order parameter. The latter implies that, depending on the data generating process, one of the two methods can attain faster convergence rates than the other. The class of multivariate Archimax copulas is examined in detail; we find that this class contains models for which the second order parameter is smaller for the BM method and vice versa. The theory is illustrated by a small simulation study.

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Section: Consequences For Estimation Precisionmentioning

confidence: 52%

On second order conditions in the multivariate block maxima and peak over threshold method

Bücher

Volgushev

Zou

2019

Journal of Multivariate Analysis

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“…in terms of a function : [12,15,19] whose analytical characterization is given in [3,34]. The stable tail dependence function of the Gumbel copula with parameter ρ ∈ (0, 1) is given, for all…”

Section: Gumbel and Galambos Brought Togethermentioning

confidence: 99%

When Gumbel met Galambos

Genest

Nešlehová

2017

Copulas and Dependence Models With Applications

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“…Archimax copulas Bivariate Archimax copulas were introduced by Capéraà et al (2000) and extended to the multivariate case with a stochastic representation by Charpentier et al (2014). They are so-called because of a connection to both Archimedean and extreme-value max-stable copulas.…”

Section: Literature Review and Examplesmentioning

confidence: 99%

Extremal dependence of random scale constructions

2019

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A bivariate random vector can exhibit either asymptotic independence or dependence between the largest values of its components. When used as a statistical model for risk assessment in fields such as finance, insurance or meteorology, it is crucial to understand which of the two asymptotic regimes occurs. Motivated by their ubiquity and flexibility, we consider the extremal dependence properties of vectors with a random scale construction (X1, X2) = R(W1, W2), with non-degenerate R > 0 independent of (W1, W2). Focusing on the presence and strength of asymptotic tail dependence, as expressed through commonly-used summary parameters, broad factors that affect the results are: the heaviness of the tails of R and (W1, W2), the shape of the support of (W1, W2), and dependence between (W1, W2). When R is distinctly lighter tailed than (W1, W2), the extremal dependence of (X1, X2) is typically the same as that of (W1, W2), whereas similar or heavier tails for R compared to (W1, W2) typically result in increased extremal dependence. Similar tail heavinesses represent the most interesting and technical cases, and we find both asymptotic independence and dependence of (X1, X2) possible in such cases when (W1, W2) exhibit asymptotic independence. The bivariate case often directly extends to higher-dimensional vectors and spatial processes, where the dependence is mainly analyzed in terms of summaries of bivariate sub-vectors. The results unify and extend many existing examples, and we use them to propose new models that encompass both dependence classes.

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Multivariate Archimax copulas

Cited by 57 publications

References 19 publications

On second order conditions in the multivariate block maxima and peak over threshold method

On second order conditions in the multivariate block maxima and peak over threshold method

When Gumbel met Galambos

Extremal dependence of random scale constructions

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