# 18-069/III (2018-09-02)

Knut Are Aastveit, Norges Bank; James Mitchell, Warwick Business School; Francesco Ravazzolo, Free University of Bozen/Bolzano; Herman van Dijk, Erasmus University, Noges Bank
Forecasting; Model Uncertainty; Density Combinations
JEL codes:
C10, C11

Increasingly, professional forecasters and academic researchers present model-based and subjective or judgment-based forecasts in economics which are accompanied by some measure of uncertainty. In its most complete form this measure is a probability density function for future values of the variables of interest. At the same time combinations of forecast densities are being used in order to integrate information coming from several sources like experts, models and large micro-data sets. Given this increased relevance of forecast density combinations, the genesis and evolution of this approach, both inside and outside economics, is explored. A fundamental density combination equation is specified which shows that various frequentist as well as Bayesian approaches give different specific contents to this density. In its most simplistic case, it is a restricted finite mixture, giving fixed equal weights to the various individual densities. The specification of the fundamental density combination is made more flexible in recent literature. It has evolved from using simple average weights to optimized weights and then to `richer' procedures that allow for time-variation, learning features and model incompleteness. The recent history and evolution of forecast density combination methods, together with their potential and benefits, are illustrated in a policy making environment of central banks.