Efficient estimation in periodic INAR(1) model: parametric case

Locally asymptotically efficient estimation for parametric PINAR(p) models

“…In order to show that our PINAR S (p) model enjoy the (LAN) property, while extending the results in Sadoun and Bentarzi (2019), we need the following definitions and notations.…”

“…Recently, the efficient estimation problem of a parametric first-order periodic integer-valued autoregressive (PINAR(1)) model was studied by Sadoun and Bentarzi (2019). Indeed, the exact difficulties to extend this result to the PINAR(p) case are to ensure that the behavior of the distribution of the efficiency influence function does not change with the change of the joint distribution of the process, and also to be able to make the necessary modifications in the parameters of the distribution of this influence function.…”

A periodic and seasonal statistical model for non-negative integer-valued time series with an application to dispensed medications in respiratory diseases

“…Even though there are many studies in the literature that focus on PC processes, most of them are dedicated to the analysis and applications for discrete time processes with continuous marginal distributions, like the PARMA model. The analysis of PC count time series was discussed in [22], [23], [24], [25], [26] and [27]. Monteiro et al [22] introduced the periodic INAR(1) (PINAR(1)) model and addressed some statistical properties of the parameter estimation together with some finite sample size investigations.…”

“…However, the paper did not explore the model in a practical problem. Sadoun and Bentarzi [23] provided efficient estimation methods of a PINAR(1) model. Morina et al [24] presented an INAR(2) model with seasonal behavior in the immigration to analyze the number of hospital emergency service arrivals caused by diseases.…”