Some Bayesian generalizations of the integer-valued autoregressive model

• Ano de defesa: 2020
• Autor(a) principal: Carvalho, Helton Graziadei de
• Tipo de documento: Tese
• Tipo de acesso: Acesso aberto
• Idioma: eng
• Instituição de defesa: Biblioteca Digitais de Teses e Dissertações da USP
• Palavras-chave em Português: Dirichlet process; Finite mixture; INAR(1); Misturas finitas; Pitman-Yor process; Processo Dirichlet; Processo Pitman-Yor
• Link de acesso: https://www.teses.usp.br/teses/disponiveis/45/45133/tde-11032020-230059/

In this thesis, we develop Bayesian generalized models for analyzing time series of counts. In our first proposal, we use a finite mixture to define the marginal distribution of the innovation process, in order to potentially account for overdispersion in the time series. Our second contribution uses a Dirichlet process at the distribution of the time-varying innovation rates, which are softly clustered through time. Finally, we examine issues of prior sensitivity in a semi-parametric extended model in which the distribution of the innovation rates follows a Pitman-Yor process. A graphical criterion to choose the Pitman-Yor base measure hyperparameters is proposed, showing explicitly that the Pitman-Yor discount parameter and the concentration parameter can interact with the chosen base measure to yield robust inferential results. The posterior distribution of the models parameters is obtained through data-augmentation schemes which allows us to obtain tractable full conditional distributions. The prediction performance of the proposed models are put to test in the analysis of two real data sets, with favorable results.