On INAR (1) models for integer time series

• Ano de defesa: 2018
• Autor(a) principal: CUNHA, Enai Taveira da
• Orientador(a): VASCONCELLOS, Klaus Leite Pinto
• Tipo de documento: Tese
• Tipo de acesso: Acesso aberto
• Idioma: eng
• Instituição de defesa: Universidade Federal de Pernambuco
• Programa de Pós-Graduação: Programa de Pos Graduacao em Estatistica
• País: Brasil
• Palavras-chave em Português: Estatística; Correção de viés
• Link de acesso: https://repositorio.ufpe.br/handle/123456789/29751

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.