p-order rounded integer-valued autoregressive (RINAR(p)) process

TL;DR

This paper introduces the RINAR(p) model, an extension of RINAR(1), for discrete-time dependent count data, offering advantages like simple innovation structure, arbitrary sign coefficients, and potential negative autocorrelation, with proven stationarity and consistent estimation.

Contribution

It proposes the RINAR(p) model as a natural extension of AR models for count data, with new features and theoretical properties, validated through simulations and real data analysis.

Findings

RINAR(p) model has simple innovation structure

Model allows negative autocorrelation and coefficients

Simulation and real data show effective performance

Abstract

An extension of the RINAR(1) process for modelling discrete-time dependent counting processes is considered. The model RINAR(p) investigated here is a direct and natural extension of the real AR(p) model. Compared to classical INAR(p) models based on the thinning operator, the new models have several advantages: simple innovation structure ; autoregressive coefficients with arbitrary signs ; possible negative values for time series ; possible negative values for the autocorrelation function. The conditions for the stationarity and ergodicity, of the RINAR(p) model, are given. For parameter estimation, we consider the least squares estimator and we prove its consistency under suitable identifiability condition. Simulation experiments as well as analysis of real data sets are carried out to assess the performance of the model.