Approximate Bayesian Model Averaging and Forecasting of Autoregressive Models

An approximate Bayesian computation approach is proposed for the inference of stationary Gaussian autoregressive models. The procedure relies on a sampling scheme that generates synthetic series and evaluates their summary statistics to build a joint approximate posterior distribution of model parameters and model order. The proposed method provides a unique framework able to perform model selection, inference on parameters as well as on prediction of future values. We show that the procedure is effective on simulated data, outperforming standard sequential forecasting methods through Bayesian model averaging.