Existence of a Periodic and Seasonal INAR Process

A spectral criterion involving the model parameters is given for the existence and uniqueness of a periodically correlated and seasonal non‐negative integer‐valued autoregressive process. The structure of the mean and covariance functions of the periodically stationary distribution of the model is d...

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Published inJournal of time series analysis Vol. 45; no. 6; pp. 980 - 1005
Main Authors Ispány, Márton, Bondon, Pascal, Reisen, Valdério Anselmo, Prezotti Filho, Paulo Roberto
Format Journal Article
LanguageEnglish
Published Oxford, UK John Wiley & Sons, Ltd 01.11.2024
Blackwell Publishing Ltd
Wiley-Blackwell
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ISSN0143-9782
1467-9892
DOI10.1111/jtsa.12746

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Summary:A spectral criterion involving the model parameters is given for the existence and uniqueness of a periodically correlated and seasonal non‐negative integer‐valued autoregressive process. The structure of the mean and covariance functions of the periodically stationary distribution of the model is derived using its implicit state‐space representation. Two infinite series representations for the process, the moving average, and the immigrant generation, are established. Based on the latter representation, a novel and parallelizable simulation method is proposed to generate the process.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
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ISSN:0143-9782
1467-9892
DOI:10.1111/jtsa.12746