Asymmetric exponential power Bayesian median autoregression with applications

Abstract

Compared with the widely used mean-based models, the prediction based on median autoregression is often more robust for time series forecasting. Motivated by the asymmetric exponential power working likelihood approach in Bayesian quantile regression, we first apply the asymmetric exponential power error to time series. The new median autoregression we proposed is more robust and can better deal with outliers. An adaptive independent Metropolis-Hastings algorithm is used for the parameter estimation. A novel, simple, and effective approximate forecasting procedure is proposed based on the Watanabe-Akaike information criterion in the framework of Bayesian model averaging. Model assessment, order selection, and out-of-sample predictive accuracy are all discussed. Finally, three examples of macroeconomic data are analyzed to show the superior performance of the proposed model.