On structure, family and parameter estimation of hierarchical Archimedean copulas

TL;DR

This paper introduces a novel method for estimating hierarchical Archimedean copulas involving multiple families, using goodness-of-fit tests, with theoretical backing and experimental validation.

Contribution

It presents a new approach for estimating HACs with different Archimedean families, expanding beyond previous methods limited to a single family.

Findings

Effective estimation of HACs with up to five different families.

The proposed method is supported by theoretical justification.

Experimental results demonstrate the approach's applicability.

Abstract

Research on structure determination and parameter estimation of hierarchical Archimedean copulas (HACs) has so far mostly focused on the case in which all appearing Archimedean copulas belong to the same Archimedean family. The present work addresses this issue and proposes a new approach for estimating HACs that involve different Archimedean families. It is based on employing goodness-of-fit test statistics directly into HAC estimation. The approach is summarized in a simple algorithm, its theoretical justification is given and its applicability is illustrated by several experiments, which include estimation of HACs involving up to five different Archimedean families.