Some Bayesian generalizations of the integer-valued autoregressive model

Author(s)

Helton Graziadei de Carvalho

• Document type: Doctoral Thesis
• Press: São Paulo.
• Institution: Universidade de São Paulo (USP). Instituto de Matemática e Estatística (IME/SBI)
• Defense date: 2020-02-17

Examining board members

Hedibert Freitas Lopes; Rinaldo Artes; Ricardo Sandes Ehlers; Luís Gustavo Esteves; Rafael Izbicki

• Advisor: Hedibert Freitas Lopes

Abstract

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. (AU)

• FAPESP's process: 17/10096-6 - Bayesian semiparametric analysis of autoregressive models
• Grantee: Helton Graziadei de Carvalho
• Support Opportunities: Scholarships in Brazil - Doctorate