The aim of this paper is to examine the weak limiting behavior of upper and lower extremes from stationary sequences satisfying dependence conditions similar to D and D' introduced by Leadbetter (Z. Wahrsch. Verw. Gebiete 28 (1974), 289-303). By establishing the convergence in distribution of an...

This article considers the problem of detecting break points for a nonstationary time series. Specifically, the time series is assumed to follow a parametric nonlinear time-series model in which the parameters may change values at fixed times. In this formulation, the number and locations of the...

This paper considers maximum likelihood estimation for the moving average parameter θ in an MA(1) model when θ is equal to or close to 1. A derivation of the limit distribution of the estimate θ_LM, defined as the largest of the local maximizers of the likelihood, is given here for the first...

Davis and Mikosch (2009a) introduced the extremogram as a flexible quantitative tool for measuring various types of extremal dependence in a stationary time series. There we showed some standard statistical properties of the sample extremogram. A major difficulty was the construction of credible...

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...

We study least absolute deviation (LAD) estimation for general autoregressive moving average time-series models that may be noncausal, noninvertible or both. For ARMA models with Gaussian noise, causality and invertibility are assumed for the parameterization to be identifiable. The assumptions,...

HASH(0x100add148)

Let Mt be the maximum of a recurrent one-dimensional diffusion up till time t. Under appropriate conditions, there exists a distribution function F such that P(Mt[less-than-or-equals, slant]x) - Ft(x)--0as t and x go to infinity. This reduces the asymptotic behavior of the maximum to that of the...

Many real-life time series exhibit clusters of outlying observations that cannot be adequately modeled by a Gaussian distribution. Heavy-tailed distributions such as the Pareto distribution have proved useful in modeling a wide range of bursty phenomena that occur in areas as diverse as finance,...