Related papers: Regularly varying time series in Banach spaces
A multivariate, stationary time series is said to be jointly regularly varying if all its finite-dimensional distributions are multivariate regularly varying. This property is shown to be equivalent to weak convergence of the conditional…
A regularly varying time series as introduced in Basrak and Segers (2009) is a (multivariate) time series such that all finite dimensional distributions are multivariate regularly varying. The extremal behavior of such a process can then be…
The goal of this paper is two-fold: 1. We review classical and recent measures of serial extremal dependence in a strictly stationary time series as well as their estimation. 2. We discuss recent concepts of heavy-tailed time series,…
The statistical theory of extremes is extended to observations that are non-stationary and not independent. The non-stationarity over time and space is controlled via the scedasis (tail scale) in the marginal distributions. Spatial…
The goal of this paper is to investigate the tools of extreme value theory originally introduced for discrete time stationary stochastic processes (time series), namely the tail process and the tail measure, in the framework of continuous…
There exist two ways of defining regular variation of a time series in a star-shaped metric space: either by the distributions of finite stretches of the series or by viewing the whole series as a single random element in a sequence space.…
The accurate estimation of scaling exponents is central in the observational study of scale-invariant phenomena. Natural systems unavoidably provide observations over restricted intervals; consequently a stationary stochastic process (time…
We study the problem of detecting and localizing multiple changes in the mean parameter of a Banach space-valued time series. The goal is to construct a collection of narrow confidence intervals, each containing at least one (or exactly…
Factor models have large potencial in the modeling of several natural and human phenomena. In this paper we consider a multivariate time series $\mb{Y}_n$, ${n\geq 1}$, rescaled through random factors $\mb{T}_n$, ${n\geq 1}$, extending some…
The goal of this paper is an exhaustive investigation of the link between the tail measure of a regularly varying time series and its spectral tail process, independently introduced in Owada and Samorodnitsky (2012) and Basrak and Segers…
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 construct a Banach rearrangement invariant norm on the measurable space for which the finiteness of this norm for measurable function (random variable) is equivalent to suitable tail (heavy tail and light tail) behavior. We investigate…
The tail measure of a regularly varying stationary time series has been recently introduced. It is used in this contribution to reconsider certain properties of the tail process and establish new ones. A new formulation of the time change…
In this paper we defined some function spaces on time scale which are Banach spaces respect to supremum norm. We study integral transformations which are carry to some important properties between mentioned above function spaces.
We study the extremes of multivariate regularly varying random fields. The crucial tools in our study are the tail field and the spectral field, notions that extend the tail and spectral processes of Basrak and Segers (2009). The spatial…
Consider two stationary time series with heavy-tailed marginal distributions. We aim to detect whether they have a causal relation, that is, if a change in one causes a change in the other. Usual methods for causal discovery are not well…
We consider estimating the shared mean of a sequence of heavy-tailed random variables taking values in a Banach space. In particular, we revisit and extend a simple truncation-based mean estimator first proposed by Catoni and Giulini. While…
Recently, neuronal avalanches have been observed to display oscillations, a phenomenon regarded as the co-existence of a scale-free behaviour (the avalanches close to criticality) and scale-dependent dynamics (the oscillations). Ordinary…
In this paper, we consider a stochastic system described by a differential equation admitting a spatially varying random coefficient. The differential equation has been employed to model various static physics systems such as elastic…
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.