Abordagem clássica e bayesiana para os modelos de séries temporais da família GARMA com aplicações para dados contínuos

Abstract

In this work, the aim was to analyze in the classic and bayesian context, the GARMA model with three different continuous distributions: Gaussian, Inverse Gaussian and Gamma. We analyzed the performance and the goodness of fit of the three models, as well as the performance of the coverage percentile. In the classic analyze we consider the maximum likelihood estimator and by simulation study, we verified the consistency, the bias and de mean square error of the models. To the bayesian approach we proposed a non-informative prior distribution for the parameters of the model, resulting in a posterior distribution, which we found the bayesian estimatives for the parameters. This study still was not found in the literature. So, we can observe that the bayesian inference showed a good quality in the analysis of the serie, which can be comprove with the last section of this work. This, consist in the analyze of a real data set corresponding in the rate of tuberculosis cases in metropolitan area of Sao Paulo. The results show that, either the classical and bayesian approach, are good alternatives to describe the behavior of the real time serie.