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Max-autogressive moving average (Max-ARMA) processes are powerful tools for modelling time series data with heavy-tailed behaviour; these are a non-linear version of the popular autoregressive moving average models. River flow data…

Methodology · Statistics 2024-03-26 Eleanor D'Arcy , Jonathan A Tawn

The present article is devoted to the semi-parametric estimation of multivariate expectiles for extreme levels. The considered multivariate risk measures also include the possible conditioning with respect to a functional covariate,…

Statistics Theory · Mathematics 2023-03-30 Elena Di Bernardino , Thomas Laloë , Cambyse Pakzad

Max-stable processes are natural models for spatial extremes because they provide suitable asymptotic approximations to the distribution of maxima of random fields. In the recent past, several parametric families of stationary max-stable…

Methodology · Statistics 2016-02-22 Raphael Huser , Marc G. Genton

We generalize the concept of extremal index of a stationary random sequence to the series scheme of identically distributed random variables with random series sizes tending to infinity in probability. We introduce new extremal indices…

Probability · Mathematics 2020-09-22 Alexey V. Lebedev

Multivariate extreme-value analysis is concerned with the extremes in a multivariate random sample, that is, points of which at least some components have exceptionally large values. Mathematical theory suggests the use of max-stable models…

Probability · Mathematics 2012-04-03 Johan Segers

In the multivariate setting, estimates of extremal risk measures are important in many contexts, such as environmental planning and structural engineering. In this paper, we propose new estimation methods for extremal bivariate return…

Methodology · Statistics 2022-10-11 C. J. R. Murphy-Barltrop , J. L. Wadsworth , E. F. Eastoe

We propose a novel strategy for multivariate extreme value index estimation. In applications such as finance, volatility and risk present in the components of a multivariate time series are often driven by the same underlying factors, such…

Statistics Theory · Mathematics 2020-03-24 Joni Virta , Niko Lietzén , Lauri Viitasaari , Pauliina Ilmonen

There is an increasing interest to understand the dependence structure of a random vector not only in the center of its distribution but also in the tails. Extreme-value theory tackles the problem of modelling the joint tail of a…

Methodology · Statistics 2014-11-04 Anna Kiriliouk , Johan Segers , Michal Warchol

This paper presents a new model for characterising temporal dependence in exceedances above a threshold. The model is based on the class of trawl processes, which are stationary, infinitely divisible stochastic processes. The model for…

Methodology · Statistics 2017-12-19 Ragnhild C. Noven , Almut E. D. Veraart , Axel Gandy

We give an overview of several aspects arising in the statistical analysis of extreme risks with actuarial applications in view. In particular it is demonstrated that empirical process theory is a very powerful tool, both for the asymptotic…

Methodology · Statistics 2015-03-19 Holger Drees

We introduce the notion of multiple extremal integrals as an extension of single extremal integrals, which have played important roles in extreme value theory. The multiple extremal integrals are formulated in terms of a product-form random…

Probability · Mathematics 2026-02-03 Shuyang Bai , Jiemiao Chen

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…

Methodology · Statistics 2021-08-03 Helena Ferreira , Marta Ferreira

The relationship between a response variable and its covariates can vary significantly, especially in scenarios where covariates take on extremely high or low values. This paper introduces a max-linear tail regression model specifically…

Methodology · Statistics 2025-02-24 Liujun Chen , Deyuan Li , Zhengjun Zhang

We investigate a family of discrete-time stationary processes defined by multiple stable integrals and renewal processes with infinite means. The model may exhibit behaviors of short-range or long-range dependence, respectively, depending…

Probability · Mathematics 2022-12-29 Shuyang Bai , Yizao Wang

This paper investigates extreme value theory for processes obtained by applying transformations to stationary Gaussian processes, also called subordinated Gaussian processes. The main contributions are as follows. First, we refine the…

Probability · Mathematics 2026-05-29 Shuyang Bai , Marie-Christine Duker

Extremal dependence between international stock markets is of particular interest in today's global financial landscape. However, previous studies have shown this dependence is not necessarily stationary over time. We concern ourselves with…

Statistical Finance · Quantitative Finance 2017-09-06 Daniela Castro Camilo , Miguel de Carvalho , Jennifer Wadsworth

Inference over tails is performed by applying only the results of extreme value theory. Whilst such theory is well defined and flexible enough in the univariate case, multivariate inferential methods often require the imposition of…

Methodology · Statistics 2017-08-11 Manuele Leonelli , Dani Gamerman

The aim of this paper is to provide models for spatial extremes in the case of stationarity. The spatial dependence at extreme levels of a stationary process is modeled using an extension of the theory of max-stable processes of de Haan and…

Statistics Theory · Mathematics 2007-06-13 Laurens de Haan , Teresa T. Pereira

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

The notion of multivariate upcrossings index of a stationary sequence ${\bf{X}}=\{(X_{n,1},\ldots,X_{n,d})\}_{n\geq 1}$ is introduced and its main properties are derived, namely the relations with the multivariate extremal index and the…

Probability · Mathematics 2010-06-09 Clara Viseu , Luísa Pereira , Ana Paula Martins , Helena Ferreira