To combine or not to combine? issues of combining forecasts

Authors

  • Franz C. Palm,

    1. Faculty of Economics and Business Administration, University of Limburg, PO Box 616, 6200 MD, Maastricht, The Netherlands
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    • Franz Palm is Professor of Econometrics at the Faculty of Economics and Business Administration, University of Limburg. He has a PhD in economics from the University of Louvain. He was a research associate at CORE and a Professor of Economics at the Free University, Amsterdam before joining the University of Limburg. His research has been concentrated on theoretical and applied econometrics with emphasis on time series analysis.

  • Arnold Zellner

    1. Graduate School of Business, University of Chicago, 1101 East 58th Street, Chicago, IL 60637. USA
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    • Arnold Zellner is the H. G. B. Alexander Distinguished Service Professor in the Graduate School of Business, University of Chicago. He has an AB in physics from Harvard, a PhD in economics from the University of California at Berkeley, and an honorary doctorate from the Autonomous University of Madrid. Before accepting an appointment at the University of Chicago in 1966, he held appointments in economics at the University of Washington in Seattle and the University of Wisconsin in Madison. His current and past research has been concentrated on theoretical and applied econometrics with emphasis on Bayesian inference and decision techniques, time series analysis, and forecasting.


Abstract

This paper addresses issues such as: Does it always pay to combine individual forecasts of a variable? Should one combine an unbiased forecast with one that is heavily biased? Should one use optimal weights as suggested by Bates and Granger over twenty years ago? A simple model which accounts for the main features of individual forecasts is put forward. Bayesian analysis of the model using noninformative and informative prior probability densities is provided which extends and generalizes results obtained by Winkler (1981) and compared with non-Bayesian methods of combining forecasts relying explicitly on a statistical model for the individual forecasts. It is shown that in some instances it is sensible to use a simple average of individual forecasts instead of using Bates and Granger type weights. Finally, model uncertainty is considered and the issue of combining different models for individual forecasts is addressed.

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