On structure, family and parameter estimation of hierarchical Archimedean copulas

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.

KEYWORDS:

• Hierarchical Archimedean copula
• copula estimation
• structure determination
• goodness-of-fit

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Jan Górecki http://orcid.org/0000-0001-5263-8637

Marius Hofert http://orcid.org/0000-0001-8009-4665

Martin Holeňa http://orcid.org/0000-0002-2536-9328

Additional information

Funding

Jan Górecki acknowledges support from the Ministry of Education, Youth and Sports of the Czech Republic within the Institutional Support for Long-term Development of a Research Organization in 2017, Marius Hofert acknowledges support from the Natural Sciences and Engineering Research Council of Canada (NSERC Discovery Grant numbers [5010] and [435844], respectively), and Martin Holeňa acknowledges support from the Czech Science Foundation (GAČR) grant [17-01251].