On INAR (1) models for integer time series
Autor(a) principal: | |
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Data de Publicação: | 2018 |
Tipo de documento: | Tese |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UFPE |
Texto Completo: | https://repositorio.ufpe.br/handle/123456789/29751 |
Resumo: | Modelling counts of events can be found in several situations of real life. For instance, the number of customers in a department store per day, monthly number of cases of some disease or the number of thunderstorms in a day. The study of integer-valued time series has grown greatly in recent decades, the reason for this is the need of appropriate models for the statistical analysis of count time series. Motivated for this, the topic of this work is integer-valued time series models. This thesis is divided into three parts, composed by three independent papers about integer-valued time series models. A brief review of the three chapters can be seen below. The skew integer-valued time series process with generalized Poisson difference distribution marginal is introduced in Chapter 2. A new thinning operator is defined as the difference of two quasi-binomial thinning operators and the new process is defined based on it. Some properties of the process like mean, variance, skewness and kurtosis are presented. The conditional expectation and variance are obtained, the autocorrelation and spectral function are derived. The moments estimation is considered and a Monte Carlo simulation is presented to study a performance of moments estimators. An application to a real data set is discussed. In Chapter 3, we consider the first-order integer-valued autoregressive process with geometric marginal distributions, NGINAR(1) process, and develop a nearly unbiased estimator for one of the parameters of the process. We consider the Yule-Walker estimators, derive the first order bias for one of the parameters and propose a new bias-adjusted estimator. Monte Carlo simulation studies are considered to analyse the behaviour of the new estimator. Finally, in Chapter 4 we introduce a first order integer-valued autoregressive process with Borel innovations based on the binomial thinning operator. This model is suitable to modelling zero truncated count time series with equidispersion, underdispersion and overdispersion. The basic properties of the process are obtained. To estimate the unknown parameters, the Yule-Walker, conditional least squares and conditional maximum likelihood methods are considered. The asymptotic distribution of conditional least squares estimators is obtained and hypothesis tests for an equidispersed model against an underdispersed or overdispersed model are formulated. A Monte Carlo simulation is presented analysing the estimators performance in finite samples. Two applications to real data are presented to show that the Borel INAR(1) model is suited to model underdispersed and overdispersed data counts. |
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CUNHA, Enai Taveira dahttp://lattes.cnpq.br/0353766630177497http://lattes.cnpq.br/4556088473868411VASCONCELLOS, Klaus Leite PintoBOURGUIGNON, Marcelo2019-03-18T21:53:13Z2019-03-18T21:53:13Z2018-02-22https://repositorio.ufpe.br/handle/123456789/29751Modelling counts of events can be found in several situations of real life. For instance, the number of customers in a department store per day, monthly number of cases of some disease or the number of thunderstorms in a day. The study of integer-valued time series has grown greatly in recent decades, the reason for this is the need of appropriate models for the statistical analysis of count time series. Motivated for this, the topic of this work is integer-valued time series models. This thesis is divided into three parts, composed by three independent papers about integer-valued time series models. A brief review of the three chapters can be seen below. The skew integer-valued time series process with generalized Poisson difference distribution marginal is introduced in Chapter 2. A new thinning operator is defined as the difference of two quasi-binomial thinning operators and the new process is defined based on it. Some properties of the process like mean, variance, skewness and kurtosis are presented. The conditional expectation and variance are obtained, the autocorrelation and spectral function are derived. The moments estimation is considered and a Monte Carlo simulation is presented to study a performance of moments estimators. An application to a real data set is discussed. In Chapter 3, we consider the first-order integer-valued autoregressive process with geometric marginal distributions, NGINAR(1) process, and develop a nearly unbiased estimator for one of the parameters of the process. We consider the Yule-Walker estimators, derive the first order bias for one of the parameters and propose a new bias-adjusted estimator. Monte Carlo simulation studies are considered to analyse the behaviour of the new estimator. Finally, in Chapter 4 we introduce a first order integer-valued autoregressive process with Borel innovations based on the binomial thinning operator. This model is suitable to modelling zero truncated count time series with equidispersion, underdispersion and overdispersion. The basic properties of the process are obtained. To estimate the unknown parameters, the Yule-Walker, conditional least squares and conditional maximum likelihood methods are considered. The asymptotic distribution of conditional least squares estimators is obtained and hypothesis tests for an equidispersed model against an underdispersed or overdispersed model are formulated. A Monte Carlo simulation is presented analysing the estimators performance in finite samples. Two applications to real data are presented to show that the Borel INAR(1) model is suited to model underdispersed and overdispersed data counts.Eventos de contagem podem ser encontrados em muitas situações práticas. Por exemplo, o número de clientes em uma loja de departamentos em um dia, o número mensal de casos de alguma doença ou o número de tempestades em um dia. O estudo de séries temporais assumindo valores inteiros cresceu muito nas recentes décadas, a razão para isto é a necessidade de modelos apropriados para a análise estatística de séries temporais de contagem. Motivado por isto, o tópico principal deste trabalho é modelos de séries temporais com valores inteiros. Esta tese é composta por três artigos, todos dentro desta área e cada capítulo pode ser lido independentemente um do outro. No segundo capítulo, definimos um novo processo autorregressivo para valores inteiros com distribuição marginal diferença de Poisson generalizadas, baseado na diferença de dois operadores "thinning" quase-binomiais. Este modelo é adequado para conjuntos de dados com valores positivos e negativos e pode ser visto como uma generalização do processo INAR(1) com marginal diferença de Poisson. Uma das vantagens da diferença de duas variáveis aleatórias com distribuição Poisson generalizada é que, em comparação com a diferença de variáveis aleatórias com distribuição Poisson, esta pode apresentar cauda curta ou cauda longa, sendo mais flexível aos dados. Algumas propriedades estatísticas básicas do processo e da distribuição condicional são obtidas. Os estimadores de Yule-Walker são considerados para a estimação dos parâmetros desconhecidos do modelo e simulações de Monte Carlo são apresentadas para o estudo da performance dos estimadores. Uma aplicação a um conjunto de dados reais é discutida para mostrar o potencial do modelo na prática. No capítulo seguinte, desenvolvemos estimadores aproximadamente não viesados para um dos parâmetros do processo autoregressivo de valores inteiros de primeira ordem com distribuição marginal geométrica, processo NGINAR(1). Consideramos os estimadores de Yule-Walker do processo, derivamos o viés de primeira ordem para um dos parâmetros do modelo e propomos um novo estimador com viés ajustado. Um estudo de simulação de Monte Carlo é considerado para analisar o comportamento do novo estimador. Finalmente, no capítulo 4 introduzimos o processo autorregressivo de primeira ordem com inovações Borel baseado no "thinning" binomial. Este modelo é adequado para séries temporais de contagem truncadas no zero que apresentam equidispersão, subdispersão e sobredispersão. Propriedades básicas do processo são obtidas. Para estimar os parâmetros desconhecidos são considerados os métodos de estimação de Yule-Walker, mínimos quadrados condicionais e máxima verossimilhança condicional. A distribuição assintótica dos estimadores de mínimos quadrados condicionais é obtida e testes de hipótese para testar um modelo equidisperso contra um subdisperso ou sobredisperso são formulados. Simulação de Monte Carlo é apresentada, analisando a performance dos estimadores em amostras finitas. Duas aplicações com dados reais são apresentadas mostrando que o modelo Borel INAR(1) é adequado para dados de contagens com subdispersão e sobredispersão.engUniversidade Federal de PernambucoPrograma de Pos Graduacao em EstatisticaUFPEBrasilAttribution-NonCommercial-NoDerivs 3.0 Brazilhttp://creativecommons.org/licenses/by-nc-nd/3.0/br/info:eu-repo/semantics/openAccessEstatísticaCorreção de viésOn INAR (1) models for integer time seriesinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/doctoralThesisdoutoradoreponame:Repositório Institucional da UFPEinstname:Universidade Federal de Pernambuco (UFPE)instacron:UFPETHUMBNAILTESE Enai Taveira da Cunha.pdf.jpgTESE Enai Taveira da Cunha.pdf.jpgGenerated Thumbnailimage/jpeg1235https://repositorio.ufpe.br/bitstream/123456789/29751/6/TESE%20Enai%20Taveira%20da%20Cunha.pdf.jpge404a3b4f86f9e4c17d1e69028684540MD56ORIGINALTESE Enai Taveira da Cunha.pdfTESE Enai Taveira da Cunha.pdfapplication/pdf766347https://repositorio.ufpe.br/bitstream/123456789/29751/1/TESE%20Enai%20Taveira%20da%20Cunha.pdfb92c1c24ae64b58e1455b8002d5633e7MD51LICENSElicense.txtlicense.txttext/plain; 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dc.title.pt_BR.fl_str_mv |
On INAR (1) models for integer time series |
title |
On INAR (1) models for integer time series |
spellingShingle |
On INAR (1) models for integer time series CUNHA, Enai Taveira da Estatística Correção de viés |
title_short |
On INAR (1) models for integer time series |
title_full |
On INAR (1) models for integer time series |
title_fullStr |
On INAR (1) models for integer time series |
title_full_unstemmed |
On INAR (1) models for integer time series |
title_sort |
On INAR (1) models for integer time series |
author |
CUNHA, Enai Taveira da |
author_facet |
CUNHA, Enai Taveira da |
author_role |
author |
dc.contributor.authorLattes.pt_BR.fl_str_mv |
http://lattes.cnpq.br/0353766630177497 |
dc.contributor.advisorLattes.pt_BR.fl_str_mv |
http://lattes.cnpq.br/4556088473868411 |
dc.contributor.author.fl_str_mv |
CUNHA, Enai Taveira da |
dc.contributor.advisor1.fl_str_mv |
VASCONCELLOS, Klaus Leite Pinto |
dc.contributor.advisor-co1.fl_str_mv |
BOURGUIGNON, Marcelo |
contributor_str_mv |
VASCONCELLOS, Klaus Leite Pinto BOURGUIGNON, Marcelo |
dc.subject.por.fl_str_mv |
Estatística Correção de viés |
topic |
Estatística Correção de viés |
description |
Modelling counts of events can be found in several situations of real life. For instance, the number of customers in a department store per day, monthly number of cases of some disease or the number of thunderstorms in a day. The study of integer-valued time series has grown greatly in recent decades, the reason for this is the need of appropriate models for the statistical analysis of count time series. Motivated for this, the topic of this work is integer-valued time series models. This thesis is divided into three parts, composed by three independent papers about integer-valued time series models. A brief review of the three chapters can be seen below. The skew integer-valued time series process with generalized Poisson difference distribution marginal is introduced in Chapter 2. A new thinning operator is defined as the difference of two quasi-binomial thinning operators and the new process is defined based on it. Some properties of the process like mean, variance, skewness and kurtosis are presented. The conditional expectation and variance are obtained, the autocorrelation and spectral function are derived. The moments estimation is considered and a Monte Carlo simulation is presented to study a performance of moments estimators. An application to a real data set is discussed. In Chapter 3, we consider the first-order integer-valued autoregressive process with geometric marginal distributions, NGINAR(1) process, and develop a nearly unbiased estimator for one of the parameters of the process. We consider the Yule-Walker estimators, derive the first order bias for one of the parameters and propose a new bias-adjusted estimator. Monte Carlo simulation studies are considered to analyse the behaviour of the new estimator. Finally, in Chapter 4 we introduce a first order integer-valued autoregressive process with Borel innovations based on the binomial thinning operator. This model is suitable to modelling zero truncated count time series with equidispersion, underdispersion and overdispersion. The basic properties of the process are obtained. To estimate the unknown parameters, the Yule-Walker, conditional least squares and conditional maximum likelihood methods are considered. The asymptotic distribution of conditional least squares estimators is obtained and hypothesis tests for an equidispersed model against an underdispersed or overdispersed model are formulated. A Monte Carlo simulation is presented analysing the estimators performance in finite samples. Two applications to real data are presented to show that the Borel INAR(1) model is suited to model underdispersed and overdispersed data counts. |
publishDate |
2018 |
dc.date.issued.fl_str_mv |
2018-02-22 |
dc.date.accessioned.fl_str_mv |
2019-03-18T21:53:13Z |
dc.date.available.fl_str_mv |
2019-03-18T21:53:13Z |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/doctoralThesis |
format |
doctoralThesis |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
https://repositorio.ufpe.br/handle/123456789/29751 |
url |
https://repositorio.ufpe.br/handle/123456789/29751 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.rights.driver.fl_str_mv |
Attribution-NonCommercial-NoDerivs 3.0 Brazil http://creativecommons.org/licenses/by-nc-nd/3.0/br/ info:eu-repo/semantics/openAccess |
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Attribution-NonCommercial-NoDerivs 3.0 Brazil http://creativecommons.org/licenses/by-nc-nd/3.0/br/ |
eu_rights_str_mv |
openAccess |
dc.publisher.none.fl_str_mv |
Universidade Federal de Pernambuco |
dc.publisher.program.fl_str_mv |
Programa de Pos Graduacao em Estatistica |
dc.publisher.initials.fl_str_mv |
UFPE |
dc.publisher.country.fl_str_mv |
Brasil |
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Universidade Federal de Pernambuco |
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