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A first-order binomial-mixed Poisson integer-valued autoregressive model with serially dependent innovations

Motivated by the extended Poisson INAR(1), which allows innovations to be serially dependent, we develop a new family of binomial-mixed Poisson INAR(1) (BMP INAR(1)) processes by adding a mixed Poisson component to the innovations of the classical Poisson INAR(1) process. Due to the flexibility of t...

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Detalles Bibliográficos
Autores principales: Chen, Zezhun, Dassios, Angelos, Tzougas, George
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Taylor & Francis 2021
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9870000/
https://www.ncbi.nlm.nih.gov/pubmed/36698548
http://dx.doi.org/10.1080/02664763.2021.1993798
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author Chen, Zezhun
Dassios, Angelos
Tzougas, George
author_facet Chen, Zezhun
Dassios, Angelos
Tzougas, George
author_sort Chen, Zezhun
collection PubMed
description Motivated by the extended Poisson INAR(1), which allows innovations to be serially dependent, we develop a new family of binomial-mixed Poisson INAR(1) (BMP INAR(1)) processes by adding a mixed Poisson component to the innovations of the classical Poisson INAR(1) process. Due to the flexibility of the mixed Poisson component, the model includes a large class of INAR(1) processes with different transition probabilities. Moreover, it can capture some overdispersion features coming from the data while keeping the innovations serially dependent. We discuss its statistical properties, stationarity conditions and transition probabilities for different mixing densities (Exponential, Lindley). Then, we derive the maximum likelihood estimation method and its asymptotic properties for this model. Finally, we demonstrate our approach using a real data example of iceberg count data from a financial system.
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spelling pubmed-98700002023-01-24 A first-order binomial-mixed Poisson integer-valued autoregressive model with serially dependent innovations Chen, Zezhun Dassios, Angelos Tzougas, George J Appl Stat Articles Motivated by the extended Poisson INAR(1), which allows innovations to be serially dependent, we develop a new family of binomial-mixed Poisson INAR(1) (BMP INAR(1)) processes by adding a mixed Poisson component to the innovations of the classical Poisson INAR(1) process. Due to the flexibility of the mixed Poisson component, the model includes a large class of INAR(1) processes with different transition probabilities. Moreover, it can capture some overdispersion features coming from the data while keeping the innovations serially dependent. We discuss its statistical properties, stationarity conditions and transition probabilities for different mixing densities (Exponential, Lindley). Then, we derive the maximum likelihood estimation method and its asymptotic properties for this model. Finally, we demonstrate our approach using a real data example of iceberg count data from a financial system. Taylor & Francis 2021-11-01 /pmc/articles/PMC9870000/ /pubmed/36698548 http://dx.doi.org/10.1080/02664763.2021.1993798 Text en © 2021 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group https://creativecommons.org/licenses/by-nc-nd/4.0/This is an Open Access article distributed under the terms of the Creative Commons Attribution-NonCommercial-NoDerivatives License (http://creativecommons.org/licenses/by-nc-nd/4.0/ (https://creativecommons.org/licenses/by-nc-nd/4.0/) ), which permits non-commercial re-use, distribution, and reproduction in any medium, provided the original work is properly cited, and is not altered, transformed, or built upon in any way.
spellingShingle Articles
Chen, Zezhun
Dassios, Angelos
Tzougas, George
A first-order binomial-mixed Poisson integer-valued autoregressive model with serially dependent innovations
title A first-order binomial-mixed Poisson integer-valued autoregressive model with serially dependent innovations
title_full A first-order binomial-mixed Poisson integer-valued autoregressive model with serially dependent innovations
title_fullStr A first-order binomial-mixed Poisson integer-valued autoregressive model with serially dependent innovations
title_full_unstemmed A first-order binomial-mixed Poisson integer-valued autoregressive model with serially dependent innovations
title_short A first-order binomial-mixed Poisson integer-valued autoregressive model with serially dependent innovations
title_sort first-order binomial-mixed poisson integer-valued autoregressive model with serially dependent innovations
topic Articles
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9870000/
https://www.ncbi.nlm.nih.gov/pubmed/36698548
http://dx.doi.org/10.1080/02664763.2021.1993798
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