Universality of Bayesian Predictions

Abstract

Given the sequential update nature of Bayes rule, Bayesian methods find natural application to prediction problems. Advances in computational methods allow to routinely use Bayesian methods in econometrics. Hence, there is a strong case for feasible predictions in a Bayesian framework. This paper studies the theoretical properties of Bayesian predictions and shows that under minimal conditions we can derive finite sample bounds for the loss incurred using Bayesian predictions under the Kullback-Leibler divergence. In particular, the concept of universality of predictions is discussed and universality is established for Bayesian predictions in a variety of settings. These include predictions under almost arbitrary loss functions, model averaging, predictions in a non stationary environment and under model miss-specification. Given the possibility of regime switches and multiple breaks in economic series, as well as the need to choose among different forecasting models, which may inevitably be miss-specified, the finite sample results derived here are of interest to economic and financial forecasting.