A Statistical Methodology for Assessing the Maximal Strength of Tail Dependence

Abstract

Several diagonal-based tail dependence indices have been suggested in the literature to quantify tail dependence. They have well-developed statistical inference theories but tend to underestimate tail dependence. For those problems when assessing the maximal strength of dependence is important (e.g., co-movements of financial instruments), the maximal tail dependence index was introduced, but it has so far lacked empirical estimators and statistical inference results, thus hindering its practical use. In the present paper, we suggest an empirical estimator for the index, explore its statistical properties, and illustrate its performance on simulated data.

Measuring non-exchangeable tail dependence using tail copulas

“…Furman et al (2015) addressed these issues and proposed variants of the TDC where the main diagonal is replaced by the path maximizing the joint tail probability. Calculation and estimation of such tail indices may not always be straightforward due to the difficulty of deriving the path of maximal dependence for a given copula C; see Sun et al (2020Sun et al ( , 2022 for recent progress on estimating such tail indices. A similar measure of non-exchangeable tail dependence limsup (u,v)↓(0,0) C(u, v)/(u + v) has also been considered in Genest and Jaworski (2021).…”

“…Calculation and estimation of such tail indices may not always be straightforward due to the difficulty of deriving the path of maximal dependence for a given copula C ; see Sun et al . (2020, 2022) for recent progress on estimating such tail indices. A similar measure of non-exchangeable tail dependence has also been considered in Genest and Jaworski (2021).…”