A0477
Title: Long range dependence in the tails
Authors: Marco Oesting - University of Stuttgart (Germany) [presenting]
Abstract: The presence or absence of long memory in time series is known to have major effects on the asymptotic properties of statistical estimators. While classical notions of long-range dependence typically rely on characteristics of the bulk of the distribution such as covariances, many common estimators in extreme value statistics are based on observations in the tails only. Motivated by this fact, we propose to separately study long memory in the extremes as given by the tail process of a regularly varying times series and the corresponding max-stable analogue. Based on a recent definition of long-range dependence that is invariant under marginal transformations, we revisit a necessary and sufficient criterion for long-range dependence of max-stable time series in terms of the pairwise extremal coefficient function. We present statistical applications of this characterization and show its effect on limit theorems which turns out to be similar to classical definitions. Furthermore, we discuss the extension of the results to processes in the max-domain of attraction.
