Bayesian Estimates in Time-Series Models

Autoregressive (AR), moving-average (MA), and autoregressive- moving average (ARMA) models are very popular in time-series analysis. Many problems of estimating their parameters and testing hypotheses are only solved asymptotically. The derivation of asymptotic results is usually not easy. An alternative approach to such problems is the Bayesian approach. It is assumed that the parameters of the models are random variables. There are theorems ensuring that under general assumptions the asymptotic posterior distribution does not depend on the prior distribution. As the derivation of the results is usually easier in the Bayesian approach, we can use this procedure particularly for the statistical analysis of more complicated models