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

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 analysi...

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Principais autores:	Borges, Patrick, Molinares, Fabio Fajardo, Bourguignon, Marcelo
Formato:	article
Idioma:	English
Publicado em:	Statistics and Probability Letters
Assuntos:	Estimation Inflated-parameter bernoulli distribution ρ-binomial thinning ρ-GINAR(1) process
Endereço do item:	https://repositorio.ufrn.br/handle/123456789/50998
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spelling	ri-123456789-509982023-01-20T17:46:23Z A geometric time series model with inflated-parameter Bernoulli counting series Borges, Patrick Molinares, Fabio Fajardo Bourguignon, Marcelo Estimation Inflated-parameter bernoulli distribution ρ-binomial thinning ρ-GINAR(1) process 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. 2023-01-20T17:43:58Z 2023-01-20T17:43:58Z 2016-08 article 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 https://repositorio.ufrn.br/handle/123456789/50998 en Acesso Aberto Statistics and Probability Letters
institution	Repositório Institucional
collection	RI - UFRN
language	English
topic	Estimation Inflated-parameter bernoulli distribution ρ-binomial thinning ρ-GINAR(1) process
spellingShingle	Estimation Inflated-parameter bernoulli distribution ρ-binomial thinning ρ-GINAR(1) process Borges, Patrick Molinares, Fabio Fajardo Bourguignon, Marcelo A geometric time series model with inflated-parameter Bernoulli counting series
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.
format	article
author	Borges, Patrick Molinares, Fabio Fajardo Bourguignon, Marcelo
author_facet	Borges, Patrick Molinares, Fabio Fajardo Bourguignon, Marcelo
author_sort	Borges, Patrick
title	A geometric time series model with inflated-parameter Bernoulli counting series
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	geometric time series model with inflated-parameter bernoulli counting series
publisher	Statistics and Probability Letters
publishDate	2023
url	https://repositorio.ufrn.br/handle/123456789/50998
work_keys_str_mv	AT borgespatrick ageometrictimeseriesmodelwithinflatedparameterbernoullicountingseries AT molinaresfabiofajardo ageometrictimeseriesmodelwithinflatedparameterbernoullicountingseries AT bourguignonmarcelo ageometrictimeseriesmodelwithinflatedparameterbernoullicountingseries AT borgespatrick geometrictimeseriesmodelwithinflatedparameterbernoullicountingseries AT molinaresfabiofajardo geometrictimeseriesmodelwithinflatedparameterbernoullicountingseries AT bourguignonmarcelo geometrictimeseriesmodelwithinflatedparameterbernoullicountingseries
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A geometric time series model with inflated-parameter Bernoulli counting series

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