Related papers: Regularly varying multivariate time series
We define a class of multivariate maxima of moving multivariate maxima, generalising the M4 processes. For these stationary multivariate time series we characterise the joint distribution of extremes and compute the multivariate extremal…
Financial time series exhibit multiscale behavior, with interaction between multiple processes operating on different timescales. This paper introduces a method for separating these processes using variance and tail stationarity criteria,…
In this paper we propose a framework that enables the study of large deviations for point processes based on stationary sequences with regularly varying tails. This framework allows us to keep track not of the magnitude of the extreme…
The notion of tail adversarial stability has been proven useful in obtaining limit theorems for tail dependent time series. Its implication and advantage over the classical strong mixing framework has been examined for max-linear processes,…
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…
We consider stationary time series $\{X_j, j \in Z\} whose finite dimensional distributions are regularly varying with extremal independence. We assume that for each $h \geq 1$, conditionally on $X_0$ to exceed a threshold tending to…
Stationarity is a very common assumption in time series analysis. A vector autoregressive process is stationary if and only if the roots of its characteristic equation lie outside the unit circle, constraining the autoregressive coefficient…
Randomly-assembled dynamical systems are theoretically predicted to be unstable upon crossing a critical threshold of complexity, as first shown by May. Yet, empirical complex systems exhibit remarkable stability, indicating the presence of…
In this paper, we consider a wide class of time-varying multivariate causal processes which nests many classic and new examples as special cases. We first prove the existence of a weakly dependent stationary approximation for our model…
Iterative imputation, in which variables are imputed one at a time each given a model predicting from all the others, is a popular technique that can be convenient and flexible, as it replaces a potentially difficult multivariate modeling…
Regular variation of distributional tails is known to be preserved by various linear transformations of some random structures. An inverse problem for regular variation aims at understanding whether the regular variation of a transformed…
We consider the problem of inference for non-stationary time series with heavy-tailed error distribution. Under a time-varying linear process framework we show that there exists a suitable local approximation by a stationary process with…
A stationary random sequence admits under some assumptions a representation as the sum of two others: one of them is a martingale difference sequence, and another is a so-called coboundary. Such a representation can be used for proving some…
Multivariate rapid variation describes decay rates of joint light tails of a multivariate distribution. We impose a local uniformity condition to control decay variation of distribution tails along different directions, and using…
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…
In a general class of one dimensional random differential equation the convergence of the distribution function of the solution to stationary state distribution is studied. In particular it is proved the boundedness respectively the…
Modeling univariate block maxima by the generalized extreme value distribution constitutes one of the most widely applied approaches in extreme value statistics. It has recently been found that, for an underlying stationary time series,…
We propose a discrete-time, finite-state stationary process that can possess long-range dependence. Among the interesting features of this process is that each state can have different long-term dependency, i.e., the indicator sequence can…
We study a linear recursion with random Markov-dependent coefficients. In a "regular variation in, regular variation out" setup we show that its stationary solution has a multivariate regularly varying distribution. This extends results…
This article primarily aims to unify the various formalisms of multivariate coefficients of variation, leveraging advanced concepts of generalized means, whether weighted or not, applied to the eigenvalues of covariance matrices. We…