Related papers: Long range dependence of heavy tailed random funct…
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…
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,…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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,…
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…
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…