Modeling time series of counts with a new class of INAR(1) model

Abstract

This paper presents a new model for a stationary non-negative first order of integer-valued random variables based on the Pegram and thinning operators. Some fundamental and regression properties of the proposed model are discussed. Maximum likelihood estimation (MLE) by the EM algorithm is applied to estimate the parameters. Numerical studies to compare the proposed model with the thinning and Pegram models and the breakdown point of MLE for the proposed model have been conducted. Finally, a real life count data set has been used to illustrate its application. Comparison with existing models by AIC showed that the proposed model is much better and illustrates its potential usefulness in empirical modeling.

A Time-Varying Mixture Integer-Valued Threshold Autoregressive Process Driven by Explanatory Variables

“…A straightforward approach in the modeling and analyzing of count time series involves creating an integer-valued autoregressive model by using thinning operators. Ever since [4] introduced the first INAR(1) time series model, which relied on the binomial thinning operator [5], it has become a prevalent method to model INAR-type models utilizing various thinning operators (see [6][7][8][9][10], among others). This approach has been extensively applied across diverse fields such as epidemiology, social sciences, economics, life sciences, and more.…”

Model-based INAR bootstrap for forecasting INAR(p) models

“…Then Al-Osh and Alzaid (1988) introduce integer moving average processes (INMA). Several other thinning operators corresponding to different kinds of counts, and in turn to different INAR models, can be implemented, as documented, for example in Weiß (2008), Scotto et al (2015) and, more recently, in Khoo et al (2017). A further generalization to semiparametric models is in Liu and Yuan (2013), while Awale et al (2017) is a recent contribution to the case in which the thinning parameter is treated as a random variable.…”

A zero-inflated geometric INAR(1) process with random coefficient

“…Recently, [21] introduced a general family of INAR(1) models with compound Poisson innovations. [8] constructed an INAR(1) model with power series innovations and [13] presented a new model based on the Pegram and thinning operators.…”