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Weighted Approximations of Tail Processes under Mixing Conditions

While the extreme value statistics for i.i.d. data is well developed, much less is known about the asymptotic behavior of statistical procedures in the presence of dependence. We establish convergence of tail empirical processes to Gaussian limits for {mixing stationary time series. As a consequence one obtains weighted approximations of the tail empirical quantile function that is based on a random sequence with marginal distribution belonging to the domain of attraction of an extreme value distribution. Moreover, the asymptotic normality is concluded for a large class of estimators of the extreme value index. These results are applied to stationary solutions of a general stochastic diierence equation.