Functionals of Clusters of Extremes

For arbitrary stationary sequences of random variables satisfying a mild mixing condition, distributional approximations are established for functionals of clusters of exceedances over a high threshold.The approximations are in terms of the distribution of the process conditionally on the event that the first variable exceeds the threshold.This conditional distribution is shown to converge to a non-trivial limit if the finite-dimensional distributions of the process are in the domain of attraction of a multivariate extreme-value distribution.In this case, therefore, limit distributions are obtained for functionals of clusters of extremes, thereby generalizing results for higher-order stationary Markov chains by S.Yun (2000), J.Appl.Probab. 37, 29 44.