Bayesian Median Autoregression for Robust Time Series Forecasting

Document pages: 19 pages

Abstract: We develop a Bayesian median autoregressive (BayesMAR) model for time seriesforecasting. The proposed method utilizes time-varying quantile regression atthe median, favorably inheriting the robustness of median regression incontrast to the widely used mean-based methods. Motivated by a working Laplacelikelihood approach in Bayesian quantile regression, BayesMAR adopts aparametric model bearing the same structure as autoregressive models byaltering the Gaussian error to Laplace, leading to a simple, robust, andinterpretable modeling strategy for time series forecasting. We estimate modelparameters by Markov chain Monte Carlo. Bayesian model averaging is used toaccount for model uncertainty, including the uncertainty in the autoregressiveorder, in addition to a Bayesian model selection approach. The proposed methodsare illustrated using simulations and real data applications. An application toU.S. macroeconomic data forecasting shows that BayesMAR leads to favorable andoften superior predictive performance compared to the selected mean-basedalternatives under various loss functions that encompass both point andprobabilistic forecasts. The proposed methods are generic and can be used tocomplement a rich class of methods that build on autoregressive models.