ABSTRACT

This chapter introduces the prior, posterior, and predictive analysis of selected autoregressive, moving average, and autoregressive-moving average models (ARMA) as well as the distributed lag model. Zellner is the only book exclusively devoted to the Bayesian analysis of time series and econometric models but deals only with autoregressive and distributed lag models. Bayesian studies of time series have been mostly made by engineers and economists. Monahan has devised a Bayesian analysis of ARMA time series models. His approach is mostly numerical in that the posterior distribution of the parameters must be specified numerically by numerical integrations. The marginal posterior distributions of the parameters of an autoregressive model are standard distributions, namely the multivariate t for the autoregressive parameters and a gamma for the precision of the white noise. Regression models with autocorrelated errors are often used with time series data and they are simple generalizations of the regression model with independent errors.