On Periodic Generalized Poisson INAR(1) Model

• Published in: Communications in statistics. Simulation and computation Vol. 53; no. 12; pp. 5926 - 5951
• Main Authors: Bentarzi, Mohamed, Souakri, Roufaida
• Format: Journal Article
• Language: English
• Published: Philadelphia Taylor & Francis 01.12.2024; Taylor & Francis Ltd
• Subjects: Autoregressive models; Autoregressive processes; Correlation; Integer-valued autoregressive; Integers; Periodic Generalized Poisson; Periodically correlated process; Periodically stationary condition; Statistical analysis
• ISSN: 0361-0918; 1532-4141
• DOI: 10.1080/03610918.2023.2205613

In this paper, we introduce a first-order Periodic Generalized Poisson Integer-Valued Autoregressive model PGPINAR ( 1 ) which has been shown to be useful to describe overdispersion, equidispersion and underdispersion feature encountered in periodically correlated Integer-Valued time series. Some probabilistic and statistical properties are established, such as the periodically correlated stationarity conditions, in the first and the second moments are provided and the closed-forms of these moments are, under these conditions, derived. Moreover, the structure of the periodic autocovariance is obtained. The estimation problem is addressed through the Yule-Walker ( YW ) , the Two-Stage Conditional Least Squares ( CLS ) and the Conditional Maximum Likelihood ( CML ) methods. The performance of these methods is done through an intensive simulation study and an application on real data set is accomplished. Keywords and phrases: Periodic Generalized Poisson, Integer-Valued Autoregressive, Periodically correlated process, periodically stationary condition.