Related papers: The extremogram: A correlogram for extreme events
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…
We introduce the concept of geometric extremal graphical models, which are defined through the gauge function of the limit set obtained from suitably scaled random vectors in light-tailed margins. For block graphs, we prove results relating…
Estimation of autocorrelations and spectral densities is of fundamental importance in many fields of science, from identifying pulsar signals in astronomy to measuring heart beats in medicine. In circumstances where one is interested in…
The extremal dependence structure of a regularly varying random vector Xis fully described by its limiting spectral measure. In this paper, we investigate how torecover characteristics of the measure, such as extremal coefficients, from the…
The extremal index is a quantity introduced in extreme value theory to measure the presence of clusters of exceedances. In the dynamical systems framework, it provides important information about the dynamics of the underlying systems. In…
In this paper we derive the asymptotic distribution of normalized residual empirical autocovariances and autocorrelations under weak assumptions on the noise. We propose new portmanteau statistics for vector autoregressive moving-average…
We derive theorems which outline explicit mechanisms by which anomalous scaling for the probability density function of the sum of many correlated random variables asymptotically prevails. The results characterize general anomalous scaling…
We consider a strictly stationary random field on the two-dimensional integer lattice with regularly varying marginal and finite-dimensional distributions. Exploiting the regular variation, we define the spatial extremogram which takes into…
We study a one-dimensional chain of harmonically coupled units in an asymmetric anharmonic soft potential. Due to nonlinear localisation of energy, this system exhibits extreme events in the sense that individual elements of the chain show…
The amount of randomness in a signal generated by physical or non-physical process can reveal important information about that process. For example, the presence of randomness in ECG signals may indicate a cardiac disease. On the hand, the…
Davis and Mikosch [7] introduced the extremogram as a flexible quantitative tool for measuring various types of extremal dependence in a stationary time series. There we showed some standard statistical properties of the sample extremogram.…
Neural networks allow us to model complex relationships between variables. We show how to efficiently find extrema of a trained neural network in regression problems. Finding the extremizing input of an approximated model is formulated as…
The extremal characteristics of random structures, including trees, graphs, and networks, are discussed. A statistical physics approach is employed in which extremal properties are obtained through suitably defined rate equations. A variety…
Several methods are available in the literature to stochastically compare random variables and random vectors. We introduce the notion of asymptotic stochastic order for random processes and define four such orders. Various properties and…
Let $\mathbf{X}(n) \in \mathbb{R}^d$ be a sequence of random vectors, where $n\in\mathbb{N}$ and $d = d(n)$. Under certain weakly dependence conditions, we prove that the distribution of the maximal component of $\mathbf{X}$ and the…
We investigate extreme value theory of a class of random sequences defined by the all-time suprema of aggregated self-similar Gaussian processes with trend. This study is motivated by its potential applications in various areas and its…
The asymptotic results that underlie applications of extreme random fields often assume that the variables are located on a regular discrete grid, identified with $\mathbb{Z}^2$, and that they satisfy stationarity and isotropy conditions.…
The extremal index is an important parameter in the characterization of extreme values of a stationary sequence. Our new estimation approach for this parameter is based on the extremal behavior under the local dependence condition…
We use point processes theory to describe the asymptotic distribution of all upper order statistics for observations collected at renewal times. As a corollary, we obtain limiting theorems for corresponding extremal processes.
The extremal index parameter theta characterizes the degree of local dependence in the extremes of a stationary time series and has important applications in a number of areas, such as hydrology, telecommunications, finance and…