A geometric time series model with inflated-parameter Bernoulli counting series

Detalhes bibliográficos
Autor(a) principal: Borges, Patrick
Data de Publicação: 2016
Outros Autores: Molinares, Fabio Fajardo, Bourguignon, Marcelo
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Institucional da UFRN
Texto Completo: https://repositorio.ufrn.br/handle/123456789/50998
Resumo: In this paper, we propose a new stationary first-order non-negative integer valued autoregressive [INAR(1)] process with geometric marginals based on a modified version of the binomial thinning operator. This new process will enable one to tackle the problem of overdispersion inherent in the analysis of integer-valued time series data that may arise due to the presence of some correlation between underlying events, heterogeneity of the population, excess to zeros, among others. In addition, it includes as special cases the geometric INAR(1) [GINAR(1)] (Alzaid and Al-Osh, 1988) and new geometric [NGINAR(1)] (Ristić et al., 2009) processes, making it be very useful in discriminating between nested models. The innovation structure of the new process is very simple. The main properties of the process are derived, such as conditional distribution, autocorrelation structure, innovation structure and jumps. The method of conditional maximum likelihood is used for estimating the process parameters. Some numerical results of the estimators are presented with a brief discussion. In order to illustrate the potential for practice of our process we apply it to a real data set.
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spelling Borges, PatrickMolinares, Fabio FajardoBourguignon, Marcelo2023-01-20T17:43:58Z2023-01-20T17:43:58Z2016-08BORGES, Patrick; MOLINARES, Fabio F.; BOURGUIGNON, Marcelo. A geometric time series model with inflated-parameter Bernoulli counting series. Statistics & Probability Letters , v. 119, p. 264-272, 2016. Disponível em: http://www.sciencedirect.com/science/article/pii/S0167715215304399?via%3Dihub. Acesso em: 07 dez. 20170167-7152https://repositorio.ufrn.br/handle/123456789/50998Statistics and Probability LettersEstimationInflated-parameter bernoulli distributionρ-binomial thinningρ-GINAR(1) processA geometric time series model with inflated-parameter Bernoulli counting seriesinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleIn this paper, we propose a new stationary first-order non-negative integer valued autoregressive [INAR(1)] process with geometric marginals based on a modified version of the binomial thinning operator. This new process will enable one to tackle the problem of overdispersion inherent in the analysis of integer-valued time series data that may arise due to the presence of some correlation between underlying events, heterogeneity of the population, excess to zeros, among others. In addition, it includes as special cases the geometric INAR(1) [GINAR(1)] (Alzaid and Al-Osh, 1988) and new geometric [NGINAR(1)] (Ristić et al., 2009) processes, making it be very useful in discriminating between nested models. The innovation structure of the new process is very simple. The main properties of the process are derived, such as conditional distribution, autocorrelation structure, innovation structure and jumps. The method of conditional maximum likelihood is used for estimating the process parameters. Some numerical results of the estimators are presented with a brief discussion. In order to illustrate the potential for practice of our process we apply it to a real data set.info:eu-repo/semantics/openAccessengreponame:Repositório Institucional da UFRNinstname:Universidade Federal do Rio Grande do Norte (UFRN)instacron:UFRNLICENSElicense.txtlicense.txttext/plain; charset=utf-81748https://repositorio.ufrn.br/bitstream/123456789/50998/2/license.txt8a4605be74aa9ea9d79846c1fba20a33MD52123456789/509982023-01-20 14:46:23.789oai:https://repositorio.ufrn.br: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Repositório de PublicaçõesPUBhttp://repositorio.ufrn.br/oai/opendoar:2023-01-20T17:46:23Repositório Institucional da UFRN - Universidade Federal do Rio Grande do Norte (UFRN)false
dc.title.pt_BR.fl_str_mv A geometric time series model with inflated-parameter Bernoulli counting series
title A geometric time series model with inflated-parameter Bernoulli counting series
spellingShingle A geometric time series model with inflated-parameter Bernoulli counting series
Borges, Patrick
Estimation
Inflated-parameter bernoulli distribution
ρ-binomial thinning
ρ-GINAR(1) process
title_short A geometric time series model with inflated-parameter Bernoulli counting series
title_full A geometric time series model with inflated-parameter Bernoulli counting series
title_fullStr A geometric time series model with inflated-parameter Bernoulli counting series
title_full_unstemmed A geometric time series model with inflated-parameter Bernoulli counting series
title_sort A geometric time series model with inflated-parameter Bernoulli counting series
author Borges, Patrick
author_facet Borges, Patrick
Molinares, Fabio Fajardo
Bourguignon, Marcelo
author_role author
author2 Molinares, Fabio Fajardo
Bourguignon, Marcelo
author2_role author
author
dc.contributor.author.fl_str_mv Borges, Patrick
Molinares, Fabio Fajardo
Bourguignon, Marcelo
dc.subject.por.fl_str_mv Estimation
Inflated-parameter bernoulli distribution
ρ-binomial thinning
ρ-GINAR(1) process
topic Estimation
Inflated-parameter bernoulli distribution
ρ-binomial thinning
ρ-GINAR(1) process
description In this paper, we propose a new stationary first-order non-negative integer valued autoregressive [INAR(1)] process with geometric marginals based on a modified version of the binomial thinning operator. This new process will enable one to tackle the problem of overdispersion inherent in the analysis of integer-valued time series data that may arise due to the presence of some correlation between underlying events, heterogeneity of the population, excess to zeros, among others. In addition, it includes as special cases the geometric INAR(1) [GINAR(1)] (Alzaid and Al-Osh, 1988) and new geometric [NGINAR(1)] (Ristić et al., 2009) processes, making it be very useful in discriminating between nested models. The innovation structure of the new process is very simple. The main properties of the process are derived, such as conditional distribution, autocorrelation structure, innovation structure and jumps. The method of conditional maximum likelihood is used for estimating the process parameters. Some numerical results of the estimators are presented with a brief discussion. In order to illustrate the potential for practice of our process we apply it to a real data set.
publishDate 2016
dc.date.issued.fl_str_mv 2016-08
dc.date.accessioned.fl_str_mv 2023-01-20T17:43:58Z
dc.date.available.fl_str_mv 2023-01-20T17:43:58Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
format article
status_str publishedVersion
dc.identifier.citation.fl_str_mv BORGES, Patrick; MOLINARES, Fabio F.; BOURGUIGNON, Marcelo. A geometric time series model with inflated-parameter Bernoulli counting series. Statistics & Probability Letters , v. 119, p. 264-272, 2016. Disponível em: http://www.sciencedirect.com/science/article/pii/S0167715215304399?via%3Dihub. Acesso em: 07 dez. 2017
dc.identifier.uri.fl_str_mv https://repositorio.ufrn.br/handle/123456789/50998
dc.identifier.issn.none.fl_str_mv 0167-7152
identifier_str_mv BORGES, Patrick; MOLINARES, Fabio F.; BOURGUIGNON, Marcelo. A geometric time series model with inflated-parameter Bernoulli counting series. Statistics & Probability Letters , v. 119, p. 264-272, 2016. Disponível em: http://www.sciencedirect.com/science/article/pii/S0167715215304399?via%3Dihub. Acesso em: 07 dez. 2017
0167-7152
url https://repositorio.ufrn.br/handle/123456789/50998
dc.language.iso.fl_str_mv eng
language eng
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
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dc.publisher.none.fl_str_mv Statistics and Probability Letters
publisher.none.fl_str_mv Statistics and Probability Letters
dc.source.none.fl_str_mv reponame:Repositório Institucional da UFRN
instname:Universidade Federal do Rio Grande do Norte (UFRN)
instacron:UFRN
instname_str Universidade Federal do Rio Grande do Norte (UFRN)
instacron_str UFRN
institution UFRN
reponame_str Repositório Institucional da UFRN
collection Repositório Institucional da UFRN
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