In this paper, we consider a simple estimator for tail dependence coefficients of a max-stable time series and show its asymptotic normality under a mild condition. The novelty of our result is that this condition does not involve mixing properties that are common in the literature. More importantly, our condition is linked to the transition between long and short range dependence (LRD/SRD) for max-stable time series. This is based on a recently proposed notion of LRD in the sense of indicators of excursion sets which is meaningfully defined for infinite-variance time series. In particular, we show that asymptotic normality with standard rate of convergence and a function of the sum of tail coefficients as asymptotic variance holds if and only if the max-stable time series is SRD.

翻译：本文考虑一个最大稳定时间序列尾部相依系数的简单估计量，并在温和条件下证明其渐近正态性。该结果的新颖之处在于该条件不涉及文献中常见的混合性质，更重要的是，该条件与最大稳定时间序列的长程/短程相依性（LRD/SRD）转变相关联。这一结论基于最近提出的关于游程集指标意义下的长程相依概念，该概念对无限方差时间序列具有明确定义。特别地，我们证明：最大稳定时间序列当且仅当具有短程相依性时，其渐近正态性成立，且收敛速度达到标准速率，渐近方差为尾部系数之和的函数。