Noncausal autoregressive models with heavy-tailed errors generate locally explosive
processes and, therefore, provide a convenient framework for modelling bubbles in …

We study non-stationary random length sequences of random variables with regularly
varying tails. Tail and extremal indexes of their maxima and linear combinations are found …

In this contribution we discuss the relation between Pickands-type constants defined for
certain Brown-Resnick stationary process $ W (t), t\in R $ as $$\mathcal {H} _W^\delta=\lim …

We study clusters of threshold exceedances caused by dependence in time series. The
clusters are defined as conglomerates containing consecutive threshold exceedances of the …

Many examples in the most diverse fields of application show the need for statistical
methods of analysis of extremes of dependent data. A crucial issue that appears when there …

We propose a new threshold selection method for nonparametric estimation of the extremal
index of stochastic processes. The discrepancy method was proposed as a data-driven …

In environmental science applications, extreme events frequently exhibit a complex spatio-
temporal structure, which is difficult to describe flexibly and estimate in a computationally …

The paper reviews the topic of extremal time series. The literature documenting the
presence of extremes in time series data is first reviewed, followed by a discussion of …

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 …

We explore the dependence structure in the sampled sequence of complex networks. We
consider randomized algorithms to sample the nodes and study extremal properties in any …