INAR(1) MODEL WITH POISSON DIFFERENCE MARGINAL DISTRIBUTION - Ahdika, Atina
Prediction of future observations for discrete random variable may be modeled by Integer-Valued Autoregressive or INAR. The interpretation of such model is described as follows: number of individuals at certain time is the sum of number of individuals who have survived (survivors) and number of arrivals. INAR model is mainly built by involving a thinning operator \ as well as certain discrete distribution for innovation. Some common distributions are usually employed such as Poisson and Geometric distributions. This book propose an INAR(1) model with Poisson Dierence (PD) marginal distribution. PD distribution is developed as the distribution of the dierence of two Poisson random variables. This model, called PD-INAR(1), is motivated by the need to accommodate negative values of the data. Parameter estimation techniques used for the model are the methods of moment and maximum likelihood. Meanwhile, a Monte Carlo simulation is carried out to illustrate some properties of the model.