@techreport{948d700ba9234068b4ad3df2968bd139,

title = "Functionals of Clusters of Extremes",

abstract = "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.",

keywords = "cluster functional, extermal index, extreme-value distribution, stationary sequence, tail sequence, threshold exceedance",

author = "J.J.J. Segers",

note = "Pagination: 22",

year = "2003",

language = "English",

volume = "2003-48",

series = "CentER Discussion Paper",

publisher = "Econometrics",

type = "WorkingPaper",

institution = "Econometrics",

}