Bayesian median autoregression for robust time series forecasting

We develop a Bayesian median autoregressive (BayesMAR) model for time series forecasting. The proposed method utilizes time-varying quantile regression at the median, favorably inheriting robustness of in contrast to widely used mean-based methods. Motivated by working Laplace likelihood approach regression, BayesMAR adopts parametric bearing same structure as models altering Gaussian error Laplace, leading simple, robust, and interpretable modeling strategy estimate parameters Markov chain Monte Carlo. averaging is account uncertainty, including uncertainty order, addition selection approach. methods are illustrated using simulations real data applications. An application U.S. macroeconomic forecasting shows that leads favorable often superior predictive performance compared selected alternatives under various loss functions encompass both point probabilistic forecasts. generic can be complement rich class build on models.