On Periodic Generalized Poisson INAR(1) Model

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 pr...

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Published inCommunications in statistics. Simulation and computation Vol. 53; no. 12; pp. 5926 - 5951
Main Authors Bentarzi, Mohamed, Souakri, Roufaida
Format Journal Article
LanguageEnglish
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
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ISSN0361-0918
1532-4141
DOI10.1080/03610918.2023.2205613

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Abstract 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.
AbstractList 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.
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.
Author Bentarzi, Mohamed
Souakri, Roufaida
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Snippet 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...
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...
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SubjectTerms Autoregressive models
Autoregressive processes
Correlation
Integer-valued autoregressive
Integers
Periodic Generalized Poisson
Periodically correlated process
Periodically stationary condition
Statistical analysis
Title On Periodic Generalized Poisson INAR(1) Model
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