The evolution of forecast density combinations in economics

Increasingly, professional forecasters and academic researchers in economics present model-based and subjective or judgment-based forecasts that are accompanied by some measure of uncertainty. In its most complete form this measure is a probability density function for future values of the variable or variables of interest. At the same time, combinations of forecast densities are being used in order to integrate information coming from multiple sources such as experts, models, and large micro-data sets. Given the increased relevance of forecast density combinations, this article explores their genesis and evolution both inside and outside economics. 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 simplest case, it is a restricted finite mixture, giving fixed equal weights to the various individual densities. The specification of the fundamental density combination equation has been made more flexible in recent literature. It has evolved from using simple average weights to optimized weights 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 the policymaking environment of central banks