International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 1, Pages 1-18
Stationary solutions for integer-valued autoregressive processes
1Department of Statistics and Operations Research, Kuwait University, P.O. Box 5969, Safat, 13060, Kuwait
2Department of Mathematics and Computer Science, University of Indianapolis, Indianapolis 46227, IN, USA
Received 5 January 2004; Revised 5 November 2004
Copyright © 2005 Emad-Eldin A. A. Aly and Nadjib Bouzar. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
The purpose of this paper is to introduce and develop a family of
-valued autoregressive processes of order () by
using the generalized multiplication of van Harn and
Steutel (1982). We obtain various distributional and regression
properties for these models. A number of stationary processes with specific marginals are presented and are shown to
generalize several existing models.