ABSTRACT

We consider a stationary generalized Ornstein-Uhlenbeck
process, whose stationary distribution is under weak regularity
conditions regularly varying. We show that this continuous-time
process is regularly varying in the sense of Hult and Lindskøg (2005).
Regular variation plays a crucial role in establishing the large sample
path behavior of a variety of statistics of generalized Ornstein-Uhlenbeck
processes. A complete analysis of the extremal behavior and the limit
behavior of the sample autocovariance function is given by means of a
point process analysis. Generalized Ornstein-Uhlenbeck processes
exhibit clusters of extremes. The behavior of the sample autocovariance
function depends on the existence of moments of the stationary distribution.