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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...
Autores principales: | , , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
Taylor & Francis
2021
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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. |
format | Online Article Text |
id | pubmed-9870000 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2021 |
publisher | Taylor & Francis |
record_format | MEDLINE/PubMed |
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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