Temporal series for random parameter models: a bayesian approach

Abstract

This paper presents a Bayesian approach to make inference about the parameters of autoregressive models. In this context, when the parameters of models are independent and vary at random we consider a hierarchical model to describe the a posteriori density of parameters. A second approach assumes that the parameters of model vary according to a first order autoregressive model. In this case, the proposed approach is seen as an extension of Kalman filter where the variances of noises are known. The models were analysed using Monte Carlo simulation techniques and the resulting samples of a posteriori densities allowed to foresee a data series through predictable densities. Ilustrations with actual data of a financial series are showed and the two models are evaluated by the quality of the prediction obtained, emphasizing the best model which represents the data.