The classical integer valued first-order autoregressive (INA- R(1)) model has been defined on the basis of Poisson innovations. This model has Poisson marginal distribution and is suitable for modeling equidispersed count data. In this paper, we introduce an modification of the INAR(1) model with geometric innovations (INARG(1)) for model- ing overdispersed count data. We discuss some structu...

The paper introduces a new autoregressive model of order one for time seriesof counts. is comprised linear as well bilinear component. These two components are governed by random coefficients. autoregression achieved using the negative binomial thinning operator. method moments and conditional maximum likelihood discussed parameter estimation. practicality presented on real data set.

• In this work we consider the problem of forecasting integer-valued time series, modelled by the INAR(1) process introduced by McKenzie (1985) and Al-Osh and Alzaid (1987). The theoretical properties and practical applications of INAR and related processes have been discussed extensively in the literature but there is still some discussion on the problem of producing coherent, i.e. integer-val...

Integer-valued autoregressive (INAR) time series form a very useful class of processes suitable to model time series of counts. In the common formulation of Du and Li (1991, JTSA), INAR models of order p share the autocorrelation structure with classical autoregressive time series. This fact allows to estimate the INAR coefficients, e.g., by Yule-Walker estimators. However, contrary to the AR c...

Abstract We start by studying first-order autoregressive negative binomial (NBD) processes. We then compare maximum likelihood and moment based estimators of the parameters of the NBD INAR(1) model and show that the degree of dependence has significant effect on the quality of the estimators. Finally, we construct NBD processes with long-range dependence by using the NBD INAR(1) processes as ba...

Integer valued AR (INAR) processes are perfectly suited for modelling count data. We consider the inclusion of explanatory variables into the INAR model to extend the applicability of INAR models and give an alternative to Poisson regression models. An efficient MCMC algorithm is constructed to analyze the model and incorporates both explanatory variable and order selection. The methodology is ...

Abstract In this paper, we propose a new type of univariate and bivariate Integer-valued autoregressive model order one (INAR(1)) to approximate linear birth death process with constant rates. Under specific parametric setting, the dynamic transition probabilities probability generating function INAR(1) will converge that as length subintervals goes 0. Due simplicity Markov structure, maximum l...