Ajuste de modelos autorregressivos, na forma de modelos lineares dinâmicos, via inferência Bayesiana

Abstract

The autoregressive models have been widely used in applications, mostly through a classical viewpoint, in which the parameters are regarded as fixed quantities, not assuming changes in time. This work aimed at fitting of autoregressive models with order 2, AR(2), specified in the form of dynamic linear models using Bayesian inference. Monte Carlo Markov Chain (MCMC) was used to obtain the estimates, via Gibbs Sampler and Forward Filtering Backward Sampling (FFBS). To evaluate the fitting, two chains with 8000 iterations each, and three different series sizes, with 200, 500 and 800 observations were sampled. The Canadian lynx series (NICHOLLS and QUIN, 1982), was fitted with different discount factors (0.90, 0.95 and 0.99), and the resulting mean square error was used to compare to the fitting using classical inference. A better fit for the model with discount equal to 0.99 was observed. One-step ahead forecasts were done to check the estimates obtained for the updated and the backward sampled series. To the latter, the fitting was better and mean square error lower. In general, it was observed a good fit of the AR(2) dynamic models via Bayesian inference, and this gives a better understanding of the fitting in different situations, both simulated and real.