Time Series: Marco Oesting
From Belle Taylor
This talk has been automatically captioned. You can remove these by pressing CC on the video toolbar.Name: Marco Oesting
Talk Title: Long Range Dependence in the Tails
Abstract: The presence or absence of long memory in time series are 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, in this talk, 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 by Kulik and Spodarev that is invariant under marginal transformations, we provide 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. Furthermore, we discuss the extension of the results to processes in the max-domain of attraction. This talk includes joint work with Vitalii Makogin, Albert Rapp and Evgeny Spodarev.
This is an invited talk at EVA 2021.