A new tractable Archimedean copula for full-range tail dependence

Abstract

Parametric copulas capable of capturing full-range tail dependence in both lower and upper tails are useful in many applications, including as pair-copula building blocks in vine copula models. However, it is challenging to create such copulas that have closed-form density functions, which limits their practical applicability in complex modeling scenarios. To the best of our knowledge, all existing full-range tail dependence copulas do not have closed-form density functions. In this paper, we propose a new Archimedean copula family, called the \emph{full-range Archimedean copula of type I} (FRA1), that captures full-range tail dependence in both tails and admits a closed-form density function. The copula has two parameters, one controlling the strength of dependence in the lower tail and the other controlling that in the upper tail. We provide results on dependence properties of the copula, and discuss how to effectively estimate the parameters based on maximum likelihood. We build a vine copula model only using the FRA1 copula, and demonstrate that the model can achieve comparable performance of an ordinary vine copula model while avoiding the need of pair-copula model selection. The new copula is also applied to data from the Medical Expenditure Panel Survey, demonstrating that an FRA1 vine model can effectively capture diverse temporal and cross-sectional dependence patterns in medical expenditures. Finally, the new copula is implemented in \texttt{CopulaOne}, an R package for full-range tail dependence copulas.