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
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.