Estimating the parameters of the binomial autoregressive process of order one I. Alwasel * , A. Alzaid, H. Al-Nachawati Department of Statistics and Operations Research, P.O. Box 2455, King Saud University, Riyadh 11451, Saudi Arabia Abstract The main objective of this paper is to compare various methods of estimation for the parameters of the ®rst-order Binomial Autoregressive Process. The small sample perfor- mance of the Yule±Walker method, conditional least squares (CLS), Gaussian estima- tion and the generalized moments method (GMM) are studied. A simulation study is presented to compare the performance of these methods. Ó 1998 Elsevier Science Inc. All rights reserved. Keywords: Binomial process; Hypergeometric; Conditional least squares; Gaussian estimation; Generalized moments method; Yule±Walker method 1. Introduction Recent research has focused on modeling discrete-time stationary processes with discrete marginal distributions. In developing such models, the integer- valued ®rst-order autoregressive (INAR (1)) process introduced by Al-Osh and Alzaid [1], Alzaid and Al-Osh [2] and McKenzie [3,4] has received great attention. The Binomial AR (1) process is de®ned as X t  S X t1   t ; t  1; 2; ... ; 1 where fS t :; t  1; 2; ...g is a sequence of independent and identically distrib- uted hypergeometric (N ; x; M ), i.e. Applied Mathematics and Computation 95 (1998) 193±204 * Corresponding author. 0096-3003/98/$19.00 Ó 1998 Elsevier Science Inc. All rights reserved. PII:S0096-3003(97)10102-3