This paper establishes necessary and sufficient conditions for the 'suitable condition' in multivariate extreme value theory, connecting extremal index, stable tail dependence functions, and Pickands dependence functions to characterize the convergence of extreme value distributions in dependent sequences.
Key findings
Establishes a necessary condition relating the multivariate extremal index to the copula structure.
Provides sufficient conditions based on regular variation properties and tail dependence coefficients.
Derives a complete characterization showing the necessary condition is also sufficient under mild regularity assumptions.
Proposes a novel dependence measure bridging asymptotic independence and dependence regimes.
Limitations & open questions
Further empirical validation in diverse real-world applications is needed.