Existence of a periodic and seasonal INAR process
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.
Mots clés
Integer-valued autoregression binomial thinning periodicity seasonality stochastic simulation Yule-Walker estimation. JEL. Primary: 60J80 62M10 Secondary: 60J10 62M15
Integer-valued autoregression
binomial thinning
periodicity
seasonality
stochastic simulation
Yule-Walker estimation. JEL. Primary: 60J80
62M10
Secondary: 60J10
62M15
Domaines
Statistiques [stat]
Fichier principal
Existence of a periodic and seasonal INAR process.pdf (1.16 Mo)
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jtsa12746-sup-0001-supinfo.pdf (619.7 Ko)
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