Generalized Mixture of Nonlinear and Nonparametric ARARCH:
Theory and Application 
Joseph Tadjuidje Kamgaing
Department of Mathematics, University of Kaiserslautern
Monday, October 9, 2006
4:10 p.m.5:00 p.m.
203 Engineering
ABSTRACT
We consider a stationary generalized OrnsteinUhlenbeck
process, whose stationary distribution is under weak regularity
conditions regularly varying. We show that this continuoustime
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 OrnsteinUhlenbeck
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 OrnsteinUhlenbeck processes
exhibit clusters of extremes. The behavior of the sample autocovariance
function depends on the existence of moments of the stationary distribution.
