Selection strategies for regular vine copulae

Czado, Claudia; Jeske, Stephan; Hofmann, Mathias

Journal de la société française de statistique, Numéro spécial sur les copules, Tome 154 (2013) no. 1, pp. 174-191.

Les grappes régulières de copules (« R-vines » en anglais) forment une famille flexible de copules de plus en plus fréquemment utilisée dans le domaine de la finance et de l’assurance. Dans un premier temps, nous présentons ces copules et nous discutons leur estimation. La classe des grappes régulières de copules étant très riche, il est crucial de disposer d’outils de sélection de modèles. Dans un deuxième temps, nous nous intéressons ainsi à un algorithme descendant de sélection de modèles récemment suggéré et nous en proposons une extension fondée sur des tests d’adéquation. L’utilisation de grappes régulières de copules et des algorithmes de sélection étudiés est enfin illustrée sur des données de concentrations chimiques.

Regular vine (R-vine) copulae are a very flexible class of multivariate copulae, which have received increasing interest in finance and insurance. We will introduce these copulae, discuss their scope and parameter estimation. Since the class of R-vines is huge, model class selection is vital. Recently a top down and a bottom up approach for model selection have been developed. We will discuss these approaches and introduce some useful extensions based on using $p$-values of goodness-of-fit tests as selection weights. The use of R-vine copulae will be illustrated for a data set involving log concentrations of chemicals in water samples. The performance of these selection procedures are investigated through simulation.

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