Modelos para Dados de Contagem com Estrutura Temporal

Abstract
In this study, we discuss the implementation of models in the class of dynamic generalized
linear models (MLDG) and the Poisson autoregressive model (PAR) in the
modelling of time series count data. Among the discussed models, we consider overdispersion
models, models with seasonal patterns and zero-inflated count data models. Our
interest is to verify the advantages and disadvantages among the different modelling approaches
and what information each of these approaches may reveal about the process
under study. All the inference procedure is made under the Bayesian approach, that is,
we attribute a prior distribution for the parameters of interest of each model in order to
obtain the posterior distribution, which in our case, is not known. Markov chain Monte
Carlo methods (MCMC) are used to obtain samples of this distribution.
In dynamic models, to obtain samples from the posterior distribution of the parameters
of interest requires some caution. There are different proposals in the literature
suggesting different ways to obtain samples of these parameters. Among the most recent
is the CUBS (Conjugate Updating Backward Sampling), proposed by Ravines et al.
(2007). In this work, we are also interested in discussing this methodology in the estimation
of parameters of dynamic models for time series count data and to investigate its
performance.
Keywords: count data, dynamic models, Poisson autoregressive model, overdispersion,
mixture models, Bayesian inference, Markov chain Monte Carlo.
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