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Stochastic volatility processes with heavy-tailed innovations are a well-known model for financial time series. In these models, the extremes of the log returns are mainly driven by the extremes of the i.i.d. innovation sequence which leads…

Probability · Mathematics 2016-03-25 Anja Janssen , Holger Drees

Moving average processes driven by exponential-tailed L\'evy noise are important extensions of their Gaussian counterparts in order to capture deviations from Gaussianity, more flexible dependence structures, and sample paths with jumps.…

Statistics Theory · Mathematics 2023-08-01 Zhongwei Zhang , David Bolin , Sebastian Engelke , Raphaël Huser

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.…

Probability · Mathematics 2015-09-03 Helena Ferreira , Luísa Pereira , Ana Paula Martins

Max-stable processes have proved to be useful for the statistical modelling of spatial extremes. Several representations of max-stable random fields have been proposed in the literature. For statistical inference it is often assumed that…

Methodology · Statistics 2011-07-25 Richard A. Davis , Claudia Klüppelberg , Christina Steinkohl

We derive exact asymptotics of $$\mathbb{P}\left(\sup_{\mathbf{t}\in {\mathcal{A}}}X(\mathbf{t})>u\right),~ \text{as}~ u\to\infty,$$ for a centered Gaussian field $X(\mathbf{t}),~ \mathbf{t}\in \mathcal{A}\subset\mathbb{R}^n$, $n>1$ with…

Probability · Mathematics 2021-11-17 Long Bai , Krzysztof Debicki , Peng Liu

Multivariate extreme value theory is concerned with modeling the joint tail behavior of several random variables. Existing work mostly focuses on asymptotic dependence, where the probability of observing a large value in one of the…

Statistics Theory · Mathematics 2022-07-11 Michaël Lalancette , Sebastian Engelke , Stanislav Volgushev

We propose a spectral clustering algorithm for analyzing the dependence structure of multivariate extremes. More specifically, we focus on the asymptotic dependence of multivariate extremes characterized by the angular or spectral measure…

Machine Learning · Statistics 2023-08-02 Marco Avella Medina , Richard A. Davis , Gennady Samorodnitsky

We introduce the extremal range, a local statistic for studying the spatial extent of extreme events in random fields on $\mathbb{R}^d$. Conditioned on exceedance of a high threshold at a location $s$, the extremal range at $s$ is the…

Statistics Theory · Mathematics 2024-11-06 Ryan Cotsakis , Elena Di Bernardino , Thomas Opitz

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…

Statistics Theory · Mathematics 2015-05-11 Helena Ferreira , Marta Ferreira

We consider stationary sequences whose marginal tail is subexponential and lies in the Gumbel Maximum domain of attraction. Due to the extremely strong dependence, their extreme values are caused by multiple big values and are clustered in…

Probability · Mathematics 2025-07-08 Zao-Li Chen

Describing the complex dependence structure of extreme phenomena is particularly challenging. To tackle this issue we develop a novel statistical algorithm that describes extremal dependence taking advantage of the inherent hierarchical…

Methodology · Statistics 2018-07-24 Sabrina Vettori , Raphaël Huser , Johan Segers , Marc G. Genton

Motivated by statistical inference problems in high-dimensional time series data analysis, we first derive non-asymptotic error bounds for Gaussian approximations of sums of high-dimensional dependent random vectors on hyper-rectangles,…

Statistics Theory · Mathematics 2024-06-05 Jinyuan Chang , Xiaohui Chen , Mingcong Wu

Extreme values modeling has attracting the attention of researchers in diverse areas such as the environment, engineering, or finance. Multivariate extreme value distributions are particularly suitable to model the tails of multidimensional…

Statistics Theory · Mathematics 2017-01-16 Helena Ferreira , Marta Ferreira

The key to successful statistical analysis of bivariate extreme events lies in flexible modelling of the tail dependence relationship between the two variables. In the extreme value theory literature, various techniques are available to…

Methodology · Statistics 2025-05-05 Emma S. Simpson , Jonathan A. Tawn

In this paper we show that the componentwise maxima ofweakly dependent bivariate stationary Gaussian triangular arrays converge in distribution after normalisation to H\"usler-Reiss distribution. Under a strong dependence assumption, we…

Probability · Mathematics 2014-12-12 E. Hashorva , Z. Weng

The analysis of spatial extremes requires the joint modeling of a spatial process at a large number of stations and max-stable processes have been developed as a class of stochastic processes suitable for studying spatial extremes. Spatial…

Methodology · Statistics 2012-09-28 Soyoung Jeon , Richard L. Smith

Extremal dependence describes the strength of correlation between the largest observations of two variables. It is usually measured with symmetric dependence coefficients that do not depend on the order of the variables. In many cases,…

Methodology · Statistics 2023-01-24 Cristina Deidda , Sebastian Engelke , Carlo De Michele

Different dependence scenarios can arise in multivariate extremes, entailing careful selection of an appropriate class of models. In bivariate extremes, the variables are either asymptotically dependent or are asymptotically independent.…

Methodology · Statistics 2015-10-30 Jennifer Wadsworth , Jonathan Tawn , Anthony Davison , Daniel Elton

The study of concomitants has recently met a renewed interest due to its applications in selection procedures. For instance, concomitants are used in ranked-set sampling, to achieve efficiency and reduce cost when compared to the simple…

Statistics Theory · Mathematics 2023-01-24 Amir Khorrami Chokami , Marie Kratz

The probability and structure of co-occurrences of extreme values in multivariate data may critically depend on auxiliary information provided by covariates. In this contribution, we develop a flexible generalized additive modeling…

Methodology · Statistics 2018-02-06 Linda Mhalla , Thomas Opitz , Valérie Chavez-Demoulin