Bayesian Analysis of ARMA Processes: Complete Sampling Based Inference Under FullLikelihoods

摘要

For a general stationary and. invertible ARMA (p,q) process, we show how to carryout a fully Bayesian analysis. Our approach is through the use of sampling based methods involving three novel aspects. First the constraints on the parameter space arising from the stationarity and invertibility conditions are handled by a convenient reparametrization to all of Euclidean (p+q)-space. Second, required sampling is facilitated by the introduction of latent variables which, though increasing the dimensionality of the problem, greatly simplifies the evaluation of the likelihood. Third, the particular sampling based approach used is a Markov chain Monte Carlo method which is a hybrid of the Gibbs sampler and the Metropolis algorithm. We also briefly show how straightforwardly the sampling based approach accommodates missing observations, outlier detection, prediction and model determination. Finally we illustrate the approach with two examples. Gibbs sampler, Invertibility, Latent variables, Metropolis algorithm, Missing values, Outliers, Prediction, Stationarity.