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

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.

💡 Research Summary

The paper introduces the p‑order Rounded Integer‑valued Autoregressive (RINAR(p)) process as a natural extension of the classical real‑valued AR(p) model to discrete‑valued time series. Unlike the traditional INAR(p) family, which relies on a thinning operator that forces autoregressive coefficients to lie in