Existence of a periodic and seasonal INAR process

Author:

Ispány Márton1ORCID,Bondon Pascal2ORCID,Reisen Valdério Anselmo234ORCID,Prezotti Filho Paulo Roberto35ORCID

Affiliation:

1. Faculty of Informatics University of Debrecen Debrecen Hungary

2. CNRS, CentraleSupélec, Laboratoire des Signaux et Systèmes Université Paris‐Saclay Gif‐sur‐Yvette France

3. Graduate Program in Environmental Engineer, Graduate Program in Economics Universidade Federal do Espírito Santo Vitoria Brazil

4. Institute of Mathematics and Statistics Universidade Federal da Bahia Salvador Brazil

5. Instituto Federal do Espírito Santo (IFES) Vitoria Brazil

Abstract

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.

Funder

Conselho Nacional de Desenvolvimento Científico e Tecnológico

Publisher

Wiley

Reference55 articles.

1. On periodic ergodicity of a general periodic mixed Poisson autoregression;Aknouche A;Statistics and Probability Letters,2018

2. First‐order integer‐valued autoregressive (INAR(1)) process;Al‐Osh MA;Journal of Time Series Analysis,1987

3. Branching Processes

4. Sparse seasonal and periodic vector autoregressive modeling;Baek C;Computational Statistics and Data Analysis,2017

5. Large sample properties of parameter estimates for periodic ARMA models;Basawa IV;Journal of Time Series Analysis,2001

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