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Tail dependence plays an essential role in the characterization of joint extreme events in multivariate data. However, most standard tail dependence parameters assume continuous margins. This note presents a form of tail dependence suitable…

Statistics Theory · Mathematics 2025-02-04 Victory Idowu

Due to globalization and relaxed market regulation, we have assisted to an increasing of extremal dependence in international markets. As a consequence, several measures of tail dependence have been stated in literature in recent years,…

Statistics Theory · Mathematics 2011-08-10 Helena Ferreira , Marta Ferreira

A framework for quantifying dependence between random vectors is introduced. With the notion of a collapsing function, random vectors are summarized by single random variables, called collapsed random variables in the framework. Using this…

Methodology · Statistics 2018-01-12 Marius Hofert , Wayne Oldford , Avinash Prasad , Mu Zhu

We consider multivariate copula-based stationary time-series under Gaussian subordination. Observed time series are subordinated to long-range dependent Gaussian processes and characterized by arbitrary marginal copula distributions. First…

Statistics Theory · Mathematics 2018-03-16 Yusufu Simayi

We propose a coefficient that measures the dependence among large values for spatial processes of maxima. Its main properties are: a) $k$ locations can be taken into account; b) it takes values in $[0,1]$ and higher values indicate stronger…

Statistics Theory · Mathematics 2015-06-22 Helena Ferreira , Luisa Pereira

Ordinal pattern dependence is a multivariate dependence measure based on the co-movement of two time series. In strong connection to ordinal time series analysis, the ordinal information is taken into account to derive robust results on the…

Statistics Theory · Mathematics 2021-06-09 Ines Nüßgen , Alexander Schnurr

In this paper we characterize the limiting behavior of sums of extreme values of long range dependent sequences defined as functionals of linear processes with finite variance. The extremal sums behave completely different by compared to…

Probability · Mathematics 2007-06-13 Rafal Kulik

We consider processes with second order long range dependence resulting from heavy tailed durations. We refer to this phenomenon as duration-driven long range dependence (DDLRD), as opposed to the more widely studied linear long range…

Statistics Theory · Mathematics 2012-09-19 Meng-Chen Hsieh , Clifford M. Hurvich , Philippe Soulier

We consider a class of stationary processes exhibiting both long-range dependence and heavy tails. Separate limit theorems for sums and for extremes have been established recently in literature with novel objects appearing in the limits. In…

Probability · Mathematics 2023-09-12 Shuyang Bai , He Tang

Long range dependence or long memory is a feature of many processes in the natural world, which provides important insights on the underlying mechanisms that generate the observed data. The usual tools available to characterize the…

Populations and Evolution · Quantitative Biology 2016-05-11 Hugo C. Mendes , Alberto Murta , R. Vilela Mendes

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

This paper is devoted to establish an invariance principle where the limit process is a multifractional Gaussian process with a multifractional function which takes its values in $(1/2,1)$. Some properties, such as regularity and local…

Probability · Mathematics 2009-09-29 Serge Cohen , Renaud Marty

We consider strictly stationary heavy tailed time series whose finite-dimensional exponent measures are concentrated on axes, and hence their extremal properties cannot be tackled using classical multivariate regular variation that is…

Statistics Theory · Mathematics 2014-10-10 Rafal Kulik , Philippe Soulier

Recently, Hammond and Sheffield introduced a model of correlated random walks that scale to fractional Brownian motions with long-range dependence. In this paper, we consider a natural generalization of this model to dimension $d\geq 2$. We…

Probability · Mathematics 2015-04-21 Hermine Biermé , Olivier Durieu , Yizao Wang

Long memory or long range dependency is an important phenomenon that may arise in the analysis of time series or spatial data. Most of the definitions of long memory of a stationary process $X=\{X_1, X_2,\cdots,\}$ are based on the…

Probability · Mathematics 2016-04-20 Yiming Ding , Xuyan Xiang

We study the limit law of a vector made up of normalized sums of functions of long-range dependent stationary Gaussian series. Depending on the memory parameter of the Gaussian series and on the Hermite ranks of the functions, the resulting…

Probability · Mathematics 2013-04-12 Murad S. Taqqu , Shuyang Bai

We establish strong invariance principles for sums of stationary and ergodic processes with nearly optimal bounds. Applications to linear and some nonlinear processes are discussed. Strong laws of large numbers and laws of the iterated…

Probability · Mathematics 2011-11-10 Wei Biao Wu

This article considers multivariate linear processes whose components are either short- or long-range dependent. The functional central limit theorems for the sample mean and the sample autocovariances for these processes are investigated,…

Probability · Mathematics 2020-02-13 Marie-Christine Düker

We consider the problem of bounding large deviations for non-i.i.d. random variables that are allowed to have arbitrary dependencies. Previous works typically assumed a specific dependence structure, namely the existence of independent…

Probability · Mathematics 2018-11-06 Christoph H. Lampert , Liva Ralaivola , Alexander Zimin

A central issue in the theory of extreme values focuses on suitable conditions such that the well-known results for the limiting distributions of the maximum of i.i.d. sequences can be applied to stationary ones. In this context, the…

Statistics Theory · Mathematics 2017-02-07 Helena Ferreira , Marta Ferreira