Tail Dependence Matrices and Tests Based on Spearman's ρ and Kendall's τ

Measuring and testing tail dependence is important in finance, insurance, and risk management. This paper proposes two tail dependence matrices based on classic rank correlation coefficients, which possess the desired population properties and interpretability. Their nonparametric estimators with strong consistency and asymptotic distributions are derived using the limit theory of U-processes. The simulation and application studies show that, compared to the tail dependence matrix based on Spearman's rho with large deviation, the Kendall-based tail dependence measure has stable variances under different tail conditions; thus, it is an effective approach to testing and quantifying tail dependence between random variables.