Efficiently sampling nested Archimedean copulas

Marius Hofert

Computational Statistics & Data Analysis, 2011, vol. 55, issue 1, 57-70

Abstract: Efficient sampling algorithms for both Archimedean and nested Archimedean copulas are presented. First, efficient sampling algorithms for the nested Archimedean families of Ali-Mikhail-Haq, Frank, and Joe are introduced. Second, a general strategy how to build a nested Archimedean copula from a given Archimedean generator is presented. Sampling this copula involves sampling an exponentially tilted stable distribution. A fast rejection algorithm is developed for the more general class of tilted Archimedean generators. It is proven that this algorithm reduces the complexity of the standard rejection algorithm to logarithmic complexity. As an application it is shown that the fast rejection algorithm outperforms existing algorithms for sampling exponentially tilted stable distributions involved, e.g., in nested Clayton copulas. Third, with the additional help of randomization of generator parameters, explicit sampling algorithms for several nested Archimedean copulas based on different Archimedean families are found. Additional results include approximations and some dependence properties, such as Kendall's tau and tail dependence parameters. The presented ideas may also apply in the more general context of sampling distributions given by their Laplace-Stieltjes transforms.

Keywords: Archimedean; copulas; Nested; Archimedean; copulas; Laplace-Stieltjes; transforms; Sampling; algorithms; Exponentially; tilted; stable; distributions (search for similar items in EconPapers)
Date: 2011
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (41)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0167-9473(10)00183-0
Full text for ScienceDirect subscribers only.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:csdana:v:55:y:2011:i:1:p:57-70

Access Statistics for this article

Computational Statistics & Data Analysis is currently edited by S.P. Azen

More articles in Computational Statistics & Data Analysis from Elsevier
Bibliographic data for series maintained by Catherine Liu ().