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Cluster indices describe extremal behaviour of stationary time series. We consider their sliding blocks estimators. Using a modern theory of multivariate, regularly varying time series, we obtain central limit theorems under conditions that…
A measure of primal importance for capturing the serial dependence of a stationary time series at extreme levels is provided by the limiting cluster size distribution. New estimators based on a blocks declustering scheme are proposed and…
We introduce the cluster index of a multivariate regularly varying stationary sequence and characterize the index in terms of the spectral tail process. This index plays a major role in limit theory for partial sums of regularly varying…
A blocks method is used to define clusters of extreme values in stationary time series. The cluster starts at the first large value in the block and ends at the last one. The block cluster measure (the point measure at clusters) encodes…
The extremes of a stationary time series typically occur in clusters. A primary measure for this phenomenon is the extremal index, representing the reciprocal of the expected cluster size. Both a disjoint and a sliding blocks estimator for…
In this paper, we investigate temporal clusters of extremes defined as subsequent exceedances of high thresholds in a stationary time series. Two meaningful features of these clusters are the probability distribution of the cluster size and…
Extremes occur in stationary regularly varying time series as short periods with several large observations, known as extremal blocks. We study cluster statistics summarizing the behavior of functions acting on these extremal blocks.…
In the regularly varying time series setting, a cluster of exceedances is a short period for which the supremum norm exceeds a high threshold. We propose to study a generalization of this notion considering short periods, or blocks, with…
The occurrence of successive extreme observations can have an impact on society. In extreme value theory there are parameters to evaluate the effect of clustering of high values, such as the extremal index. The estimation of the extremal…
Any limiting point process for the time normalized exceedances of high levels by a stationary sequence is necessarily compound Poisson under appropriate long range dependence conditions. Typically exceedances appear in clusters. The…
It is well known that the distribution of extreme values of strictly stationary sequences differ from those of independent and identically distributed sequences in that extremal clustering may occur. Here we consider non-stationary but…
Motivated by examples from extreme value theory we introduce the general notion of a cluster process as a limiting point process of returns of a certain event in a time series. We explore general invariance properties of cluster processes…
We consider disjoint and sliding blocks estimators of cluster indices for multivariate, regularly varying time series in the Peak-over-Threshold framework. We aim to provide a complete description of the limiting behaviour of these…
We re-consider Leadbetter's extremal index for stationary sequences. It has interpretation as reciprocal of the expected size of an extremal cluster above high thresholds. We focus on heavy-tailed time series, in particular on regularly…
In extreme value statistics for stationary sequences, blocks estimators are usually constructed by using disjoint blocks because exceedances over high thresholds of different blocks can be assumed asymptotically independent. In this paper…
Let $(X_{n,i})_{1\le i\le n,n\in\mathbb{N}}$ be a triangular array of row-wise stationary $\mathbb{R}^d$-valued random variables. We use a "blocks method" to define clusters of extreme values: the rows of $(X_{n,i})$ are divided into $m_n$…
Meta-analyses frequently include trials that report multiple effect sizes based on a common set of study participants. These effect sizes will generally be correlated. Cluster-robust variance-covariance estimators are a fruitful approach…
In this work a robust clustering algorithm for stationary time series is proposed. The algorithm is based on the use of estimated spectral densities, which are considered as functional data, as the basic characteristic of stationary time…
This study focuses on exploring the use of local interpretability methods for explaining time series clustering models. Many of the state-of-the-art clustering models are not directly explainable. To provide explanations for these…
We study the problem of clustering sequences of unlabeled point sets taken from a common metric space. Such scenarios arise naturally in applications where a system or process is observed in distinct time intervals, such as biological…