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Article Dans Une Revue Journal of Time Series Analysis Année : 2024

Existence of a periodic and seasonal INAR process

Márton Ispány
Pascal Bondon
Valdério Anselmo Reisen
Paulo Roberto Prezotti Filho

Résumé

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.
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Dates et versions

hal-04581441 , version 1 (23-05-2024)

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Márton Ispány, Pascal Bondon, Valdério Anselmo Reisen, Paulo Roberto Prezotti Filho. Existence of a periodic and seasonal INAR process. Journal of Time Series Analysis, 2024, ⟨10.1111/jtsa.12746⟩. ⟨hal-04581441⟩
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