Optimal Prediction Pools
AbstractA 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.
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Bibliographic InfoPaper provided by The Rimini Centre for Economic Analysis in its series Working Paper Series with number 22-08.
Date of creation: Jan 2008
Date of revision: Jan 2008
forecasting; GARCH; log scoring; Markov mixture; model combination; S&P 500 returns; stochastic volatility;
Other versions of this item:
- C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
- C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
This paper has been announced in the following NEP Reports:
- NEP-ALL-2008-09-13 (All new papers)
- NEP-ECM-2008-09-13 (Econometrics)
- NEP-ETS-2008-09-13 (Econometric Time Series)
- NEP-FOR-2008-09-13 (Forecasting)
- NEP-ORE-2008-09-13 (Operations Research)
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