Econometric Forecasting Using Linear Regression and Belief Functions

Abstract

We describe a method for quantifying the uncertainty in statistical forecasts using belief functions. This method consists in two steps. In the estimation step, uncertainty on the model parameters is described by a consonant belief function defined from the relative likelihood function. In the prediction step, parameter uncertainty is propagated through an equation linking the quantity of interest to the parameter and an auxiliary variable with known distribution. This method allows us to compute a predictive belief function that is an alternative to both prediction intervals and Bayesian posterior predictive distributions. In this paper, the feasibility of this approach is demonstrated using a model used extensively in econometrics: linear regression with first order autoregressive errors. Results with macroeconomic data are presented.