Two-Threshold-Variable Integer-Valued Autoregressive Model

Poisson Difference Integer Valued Autoregressive Model of Order one

This paper aims to model integer valued time series with possible negative values and either positive or negative correlations by introducing the Poisson difference integer valued autoregressive model of order one. This model has Poisson difference marginal distribution and is defined by a new operator called the extended binomial thinning operator. It includes previous integer valued autoregre...

Conditional Maximum Likelihood Estimation of the First-Order Spatial Integer-Valued Autoregressive (SINAR(1,1)) Model

‎Recently a first-order Spatial Integer-valued Autoregressive‎ ‎SINAR(1,1) model was introduced to model spatial data that comes‎ ‎in counts citep{ghodsi2012}‎. ‎Some properties of this model‎ ‎have been established and the Yule-Walker estimator has been‎ ‎proposed for this model‎. ‎In this paper‎, ‎we introduce the...

Stationary solutions for integer-valued autoregressive processes

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 ...

Threshold Variable Determination and Threshold Variable Driven Switching Autoregressive Models

In this paper we propose a new class of nonlinear time series models, the threshold variable driven switching autoregressive models. It is a hierarchical model that combines two important nonlinear time series models, the threshold autoregressive (AR) models and the random switching AR models. The underlying time series process switches between two (or more) different linear models. The switchi...

A bivariate first-order signed integer-valued autoregressive process