On forecasting with univariate autoregressive processes: a bayesian approach

Using a normal-gamma prior density for the parameters of a p-th order autoregressive process, the Bayesian predictive density of k future observations is derived and it is shown that it is the product of k univariate t densities. Our results are illustrated with one step ahead forecasts employing AR(1) and AR(2) models with a vague prior density for the parameters.