الفهرس 
CHAPTER 1Only 14 pages are availabe for public view
 |  | from | 103 |  |  |
| | | from | 103 | | |
Abstract
The integer valued time series has emerged as an important area of research in
many elds such as medicine, insurance, nance, economics and communications.
Most of the models of integer valued time series arises are linear. However, in practice,
there are many data cannot be adequately represented by linear models; hence the
necessity of nonlinear models. The majority of these linear models are that the
autoregressive models of order one (INAR(1)) with di¤erent marginal distributions.
This class of models could be used tomodel some speci c counting processes. In this
thesis we extend the class of integer valued bilinear model of order one (INBL(1,0,1,1))
introduced by Doukhan, et al (2006) to more general INBL models.
In Chapter 1, we present some fundamental concepts of time series such as sta-
tionarity, the autocovariance and autocorrelation functions, linear time series models,
autoregressive models (AR), moving average models (MA), the mixed autoregressive
moving average model (ARMA), and bilinear time series models.
Chapter 2, is a short review of the real integer valued time series models. Brief pre- sentations of integer valued autoregressive time series models of order one (INAR(1))with Poisson, geometric and negative binomial marginals and thinning are given.Some INAR(p) are also discussed.
In chapter 3, we summaraize the Integer Valued Bilinear Model INBL(1; 0; 1; 1)
from Doukhan, et al (2006). We generalized this model into INBL(p; 0; p; 1) andobserving that all its properties.In chapter 4, We derive the Integer Valued Bilinear Model INBL(2; 0; 1; 1); and INBL(2; 0; 2; 1): Also we give the estimation of the model parameters by Yule-Walker estimators. Some Monte Carlo results and applications using real data are given.