International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 1, Pages 1-18
doi:10.1155/IJMMS.2005.1

Stationary solutions for integer-valued autoregressive processes

Emad-Eldin A. A. Aly1 and Nadjib Bouzar2

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.

Abstract

The purpose of this paper is to introduce and develop a family of ℤ+-valued autoregressive processes of order p (INAR(p)) by using the generalized multiplication ⊙F of van Harn and Steutel (1982). We obtain various distributional and regression properties for these models. A number of stationary INAR(p) processes with specific marginals are presented and are shown to generalize several existing models.