Bayesian analysis of autoregressive moving average processes with unknown orders

A Bayesian model selection for modelling a time series by an autoregressive–moving–average model (ARMA) is presented. The posterior distribution of unknown parameters and the selected orders are obtained by the Markov chain Monte Carlo (MCMC) method. An MCMC algorithm that represents the parameters of the model as a point process has been implemented. The method is illustrated on simulated series and a real dataset.