Assessing the Quality of Prediction Baykal: Bayesian Prediction by Kalman Filtering

Abstract

In Bayesian statistics for prediction a complete predictive density is calculated. This is an ideal means to asses the quality of prediction, as arbitrary measures of dispersion can be computed. The predictive density not only reflects the randomness of the residuals, but also takes into account the uncertainty of parameter estimates. In this paper a method (BAYKAL) is presented, which computes the predictive density by a Monte Carlo integration technique using the Kalman filter. BAYKAL is applicable to linear models with various features including simultaneous equations, observation errors, and correlated residuals. Apriori informations can be incorporated in a flexible way. Complete marginal densities, various parameters of these densities and measures of numerical errors can be obtained. For three small models the BAYKAL - predictions are compared with usual econometric predictions. The results indicate that the dispersion of BAYKAL predictions are always larger than the dispersion of the corresponding econometric predictions, which neglect the uncertainty of the parameters.