Inferência, previsão e suavização em modelos estruturais Gaussianos e não-Gaussianos

Abstract

This dissertation is dedicated to the discussion of the methodology of structural models, also known as dynamic models, for modeling time series. In this work, the main objective is the comparison of classical and Bayesian estimators in order to make inferences about the parameters of the model. For this purpose, the computational techniques bootstrap, in the classical approach, and Markov chain Monte Carlo (MCMC), in the Bayesian approach, are used. Through Monte Carlo simulations, the bias and the mean square error of the maximum likelihood and Bayesian estimators are compared. Evaluating the point estimators, the maximum likelihood and the posterior mode estimators present in general better performance. It can be also checked that the bootstrap estimates mimics well the behavior of the maximum likelihood estimates in the Monte Carlo replications of models. Besides, asymptotic and bootstrap confidence intervals and credibility intervals for the hyperparameters are built, and they are compared with respect to the coverage rate and width. The credibility intervals show a better performance than the classical confidence intervals especially the asymptotic ones that, in some cases, present limits that go beyond the parametric space, mainly for small time series. This work also presents an extension of the methodology to model series that possesses structural breaks, using transfer functions. In the final part, a proposal of a new family of non-gaussian models is presented. As illustration of the methodologies, applications to some real time series are performed.