Goodness-of-fit Tests For Elliptical And Independent Copulas Through Projection Pursuit

TL;DR

This paper introduces projection pursuit-based goodness-of-fit tests for elliptical and independent copulas, enabling identification of their axis systems and exact copula values, supported by simulations and real data applications.

Contribution

It develops a novel projection pursuit methodology for testing copula goodness-of-fit, specifically for elliptical and independent copulas, with practical implementation and validation.

Findings

Effective identification of copula axis systems.

Accurate estimation of copula values in identified bases.

Validated through simulations and real data applications.

Abstract

Two goodness-of-fit tests for copulas are being investigated. The first one deals with the case of elliptical copulas and the second one deals with independent copulas. These tests result from the expansion of the projection pursuit methodology we will introduce in the present article. This method enables us to determine on which axis system these copulas lie as well as the exact value of these very copulas in the basis formed by the axes previously determined irrespective of their value in their canonical basis. Simulations are also presented as well as an application to real datasets.