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Optimal Prediction Pools

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Author Info
John Geweke () (Departments of Statistics and Economics, University of Iowa, Iowa City, IA, USA.)
Gianni Amisano () (European Central Bank, Kaiserstrasse 29, D-60311 Frankfurt am Main, Germany.)

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Abstract

A prediction model is any statement of a probability distribution for an outcome not yet observed. This study considers the properties of weighted linear combinations of n prediction models, or linear pools, evaluated using the conventional log predictive scoring rule. The log score is a concave function of the weights and, in general, an optimal linear combination will include several models with positive weights despite the fact that exactly one model has limiting posterior probability one. The paper derives several interesting formal results: for example, a prediction model with positive weight in a pool may have zero weight if some other models are deleted from that pool. The results are illustrated using S&P 500 returns with prediction models from the ARCH, stochastic volatility and Markov mixture families. In this example models that are clearly inferior by the usual scoring criteria have positive weights in optimal linear pools, and these pools substantially outperform their best components. JEL Classification: C11, C53.

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Publisher Info
Paper provided by European Central Bank in its series Working Paper Series with number 1017.

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Length: 37 pages
Date of creation: Mar 2009
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Handle: RePEc:ecb:ecbwps:20091017

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Related research
Keywords: forecasting; GARCH; log scoring; Markov mixture; model combination; S&P 500 returns; stochastic volatility.;

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This paper has been announced in the following NEP Reports: References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
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  2. Michael Clements, 2006. "Evaluating the survey of professional forecasters probability distributions of expected inflation based on derived event probability forecasts," Empirical Economics, Springer, vol. 31(1), pages 49-64, March. [Downloadable!] (restricted)
  3. Corradi, Valentina & Swanson, Norman R., 2006. "Predictive density and conditional confidence interval accuracy tests," Journal of Econometrics, Elsevier, vol. 135(1-2), pages 187-228. [Downloadable!] (restricted)
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  4. Quandt, Richard E, 1974. "A Comparison of Methods for Testing Nonnested Hypotheses," The Review of Economics and Statistics, MIT Press, vol. 56(1), pages 92-99, February. [Downloadable!] (restricted)
  5. Kenneth F. Wallis, 2005. "Combining Density and Interval Forecasts: A Modest Proposal," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 67(s1), pages 983-994, December. [Downloadable!] (restricted)
  6. Gneiting, Tilmann & Raftery, Adrian E., 2007. "Strictly Proper Scoring Rules, Prediction, and Estimation," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 359-378, March. [Downloadable!] (restricted)
  7. Clemen, Robert T. & Murphy, Allan H. & Winkler, Robert L., 1995. "Screening probability forecasts: contrasts between choosing and combining," International Journal of Forecasting, Elsevier, vol. 11(1), pages 133-145, March. [Downloadable!] (restricted)
  8. John Geweke & Gianni Amisano, 2007. "Hierarchical Markov Normal Mixture Models with Applications to Financial Asset Returns," Working Papers 0705, University of Brescia, Department of Economics. [Downloadable!]
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  9. Emir Shuford & Arthur Albert & H. Edward Massengill, 1966. "Admissible probability measurement procedures," Psychometrika, Springer, vol. 31(2), pages 125-145, June. [Downloadable!] (restricted)
  10. Corradi, Valentina & Swanson, Norman R., 2006. "Predictive Density Evaluation," Handbook of Economic Forecasting, Elsevier. [Downloadable!] (restricted)
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  11. Christoffersen, Peter F, 1998. "Evaluating Interval Forecasts," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 841-62, November.
  12. Granger, C. W. J. & White, Halbert & Kamstra, Mark, 1989. "Interval forecasting : An analysis based upon ARCH-quantile estimators," Journal of Econometrics, Elsevier, vol. 40(1), pages 87-96, January. [Downloadable!] (restricted)
  13. Hall, Stephen G. & Mitchell, James, 2007. "Combining density forecasts," International Journal of Forecasting, Elsevier, vol. 23(1), pages 1-13. [Downloadable!] (restricted)
  14. Geweke, John, 2001. "Bayesian econometrics and forecasting," Journal of Econometrics, Elsevier, vol. 100(1), pages 11-15, January. [Downloadable!] (restricted)
  15. Jacquier, Eric & Polson, Nicholas G & Rossi, Peter E, 1994. "Bayesian Analysis of Stochastic Volatility Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(4), pages 371-89, October.
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(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. John Geweke & Gianni Amisano, 2008. "Comparing and evaluating Bayesian predictive distributions of asset returns," Working Paper Series 969, European Central Bank. [Downloadable!]
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