When a copula is archimax

Wysocki, Włodzimierz

doi:10.1016/j.spl.2012.09.003

Cited by 2 publications

(1 citation statement)

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“…Meanwhile, if ϕ ( t ) = exp(− t ), then the copula reduces to an EV copula, and thus the name Archimax. More information on Archimax copulae and their generalizations to higher dimensions can be found in Bacigal et al (2011), Wysocki (2013), Mesiar and Jágr (2013), and Charpentier et al (2014). Genest and Jaworski (2020) observe how a prespecification of the degree of association affects the size of the class of Archimax copulae.…”

Section: Bivariate Copulaementioning

confidence: 99%

Copulae: An overview and recent developments

Größer

Okhrin

2021

WIREs Computational Stats

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Over the decades that have passed since they were introduced, copulae still remain a very powerful tool for modeling and estimating multivariate distributions. This work gives an overview of copula theory and it also summarizes the latest results. This article recalls the basic definition, the most important cases of bivariate copulae, and it then proceeds to a sketch of how multivariate copulae are developed both from bivariate copulae and from scratch. Regarding higher dimensions, the focus is on hierarchical Archimedean, vine, and factor copulae, which are the most often used and most flexible ways to introduce copulae to multivariate distributions. We also provide an overview of how copulae can be used in various fields of data science, including recent results. These fields include but are not limited to time series and machine learning. Finally, we describe estimation and testing methods for copulae in general, their application to the presented copula structures, and we give some specific testing and estimation procedures for those specific copulae.

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