Tree-based conditional copula estimation

Bonacina Francesco (), Lopez Olivier () and Thomas Maud ()
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Bonacina Francesco: Sorbonne Université, CNRS, Laboratoire de Probabilités, Statistique et Modélisation, LPSM, 4 place Jussieu, F-75005 Paris, France
Lopez Olivier: CREST Laboratory, CNRS, Groupe des Écoles Nationales d’Économie et Statistique, Ecole Polytechnique, Institut Polytechnique de Paris, 5 avenue Henry Le Chatelier 91120 Palaiseau, France
Thomas Maud: Sorbonne Université, CNRS, Laboratoire de Probabilités, Statistique et Modélisation, LPSM, 4 place Jussieu, F-75005 Paris, France

Dependence Modeling, 2025, vol. 13, issue 1, 25

Abstract: This article proposes a regression tree procedure to estimate conditional copulas. The associated algorithm determines classes of observations based on covariate values and fits a simple parametric copula model on each class. The association parameter changes from one class to another, allowing for non-linearity in the dependence structure modeling. It also allows the definition of classes of observations on which the so-called “simplifying assumption” holds reasonably well. When considering observations belonging to a given class separately, the association parameter no longer depends on the covariates according to our model. In this article, we derive asymptotic consistency results for the regression tree procedure and show that the proposed pruning methodology, i.e., the model selection techniques selecting the appropriate number of classes, is optimal in some sense. Simulations provide finite sample results, and an analysis of data of cases of human influenza presents the practical behavior of the procedure.

Keywords: conditional copula; regression trees; asymptotic theory (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:vrs:demode:v:13:y:2025:i:1:p:25:n:1001

DOI: 10.1515/demo-2024-0010

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