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In this paper, we consider a simple estimator for tail dependencecoefficients of a max-stable time series and show its asymptotic normalityunder a mild condition. The novelty of our result is that this condition doesnot involve mixing properties that are common in the literature. Moreimportantly, our condition is linked to the transition between long and shortrange dependence (LRD/SRD) for max-stable time series. This is based on arecently proposed notion of LRD in the sense of indicators of excursion setswhich is meaningfully defined for infinite-variance time series. In particular,we show that asymptotic normality with standard rate of convergence and afunction of the sum of tail coefficients as asymptotic variance holds if andonly if the max-stable time series is SRD.

Long Memory of Max-Stable Time Series as Phase Transition: Asymptotic Behaviour of Tail Dependence Estimators