The Evolution of Forecast Density Combinations in Economics

Tinbergen Institute Discussion Paper 2018-069/III

47 Pages Posted: 12 Sep 2018

See all articles by Knut Are Aastveit

Knut Are Aastveit

Norges Bank

James Mitchell

Warwick Business School

Francesco Ravazzolo

Free University of Bozen-Bolzano

H. K. van Dijk

Tinbergen Institute; Econometric Institute

Date Written: August 27, 2018


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.

Keywords: Forecasting, Model Uncertainty, Density Combinations

JEL Classification: C10, C11

Suggested Citation

Aastveit, Knut Are and Mitchell, James and Ravazzolo, Francesco and van Dijk, Herman K., The Evolution of Forecast Density Combinations in Economics (August 27, 2018). Tinbergen Institute Discussion Paper 2018-069/III, Available at SSRN: or

Knut Are Aastveit (Contact Author)

Norges Bank ( email )

P.O. Box 1179
Oslo, N-0107

James Mitchell

Warwick Business School ( email )

Coventry CV4 7AL
United Kingdom

Francesco Ravazzolo

Free University of Bozen-Bolzano ( email )

Sernesiplatz 1
Bozen-Bolzano, BZ 39100

Herman K. Van Dijk

Tinbergen Institute ( email )

Gustav Mahlerplein 117
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+31104089031 (Fax)


Econometric Institute ( email )

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