Unsupervised Learning Applied to the Grouped t-Copula or the Modeling of Real-Life Dependence

28 Pages Posted: 17 Jan 2018

See all articles by Loïc Brin

Loïc Brin

Société Générale

Pierre Clauss

Société Générale; Université d'Évry - Centre D'Etudes des Politiques Economiques et de L'Emploi (EPEE)

François Crénin

Société Générale

Sophie Lavaud

Societe Generale

Jiali Xu

Societe Generale

Date Written: January 11, 2018

Abstract

Grouped t-copulas were introduced by Embrechts et al. (1999) and Fang et al. (2002) to address the inability of Gaussian copulas to model non-linear dependencies and of t-copulas to model heterogeneous tail-dependencies. These heterogeneous tail-dependencies can be observed in many fields (finance, hydrology, meteorology). Nonetheless, the use of grouped t-copulas comes at the price of a higher number of parameters to fit, and the necessity to form a priori unknown groups which variables' tail-dependencies are the same. This paper takes up these two challenges by providing an unsupervised method based on the bootstrapped estimates of individual t-copulas to form the groups, and a procedure to fit the grouped t-copula once the groups are known by combining the four-step procedures introduced in Brin et Xu (2016) with a bootstrap on the MLE of the grouped t-copula. This methodology gives good results on simulated data sets as soon as the number of observations is large enough (above 1000).

Keywords: grouped t-copula, statistical clustering, correlation and dependence measures, tail dependence, copula calibration

Suggested Citation

Brin, Loïc and Clauss, Pierre and Crénin, François and Lavaud, Sophie and Xu, Jiali, Unsupervised Learning Applied to the Grouped t-Copula or the Modeling of Real-Life Dependence (January 11, 2018). Available at SSRN: https://ssrn.com/abstract=3100048 or http://dx.doi.org/10.2139/ssrn.3100048

Loïc Brin (Contact Author)

Société Générale ( email )

Pierre Clauss

Société Générale ( email )

Université d'Évry - Centre D'Etudes des Politiques Economiques et de L'Emploi (EPEE) ( email )

Boulevard Francois Mitterrand
F-91025 Evry Cedex
France

François Crénin

Société Générale ( email )

52 Place de l'Ellipse
La Défense, 92000
France

Sophie Lavaud

Societe Generale ( email )

52 Place de l'Ellipse
La Défense, 92000
France

Jiali Xu

Societe Generale ( email )

52 Place de l'Ellipse
La Défense, 92000
France

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