This article studies theory and inference of an observation-driven model for time series of counts. It is assumed that the observations follow a Poisson distribution conditioned on an accompanying intensity process, which is equipped with a two-regime structure according to the magnitude of the...

Continuous-time autoregressive moving average (CARMA) processes with a nonnegative kernel and driven by a nondecreasing Lévy process constitute a useful and very general class of stationary, nonnegative continuous-time processes that have been used, in particular, for the modeling of stochastic...

Assuming that {(Un,Vn)} is a sequence of càdlàg processes converging in distribution to (U,V) in the Skorohod topology, conditions are given under which {∬fn(β,u,v)dUndVn} converges weakly to ∬f(β,x,y)dUdV in the space C(R), where fn(β,u,v) is a sequence of “smooth” functions...

We study the joint limit distribution of the k largest eigenvalues of a p×p sample covariance matrix XXT based on a large p×n matrix X. The rows of X are given by independent copies of a linear process, Xit=∑jcjZi,t−j, with regularly varying noise (Zit) with tail index α∈(0,4). It is...

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, including regular variation and max-stable processes.

We consider estimates motivated by extreme value theory for the correlation parameter of a first-order autoregressive process whose innovation distribution F is either positive or supported on a finite interval. In the positive support case, F is assumed to be regularly varying at zero, whereas...

We consider a simple bilinear process Xt=aXt-1+bXt-1Zt-1+Zt, where (Zt) is a sequence of iid N(0,1) random variables. It follows from a result by Kesten (1973, Acta Math. 131, 207-248) that Xt has a distribution with regularly varying tails of index [alpha]0 provided the equation Ea+bZ1u=1 has...