Robust Bayesian model selection for autoregressive processes with additive outliers

Autoregressive (AR) models of order k are often used for forecasting and control of time series, as well as for the estimation of functionals such as the spectrum. Here we propose a method that consists of calculating the posterior probabilities of the competing AR(k) models in a way that is robust to outliers, and then obtaining the predictive distributions of quantities of interest, such as future observations and the spectrum, as a weighted average of the predictive distributions conditional on each model. This method is based on the idea of robust Bayes factors, calculated by replacing the likelihood for the nominal model by a robust likelihood It draws on and synthesizes several recent research advances, namely robust filtering and the Laplace method for integrals, modified to take account of the finite range of the parameters. The method performs well in simulation experiments and on real and artificial data. Software is available from StatLib.