Corrected Forecast Combinations

2026-01-15

AI Summary

This study addresses the instability of optimal combination weights and poor forecasting performance often caused by serial correlation in forecast errors. The authors propose a bias-correction approach that incorporates the predictable component of the previous period’s forecast error into the next-period prediction. Within a conditional risk minimization framework, they formalize this method by decomposing forecast errors into a predictable part and a new innovation term. Combining generalized least squares, they jointly estimate the combination weights and the error covariance structure to effectively account for temporal dependence. Empirical results using Survey of Professional Forecasters data show that applying a correction coefficient of approximately 0.5 substantially improves forecast accuracy, restoring competitiveness to previously underperforming optimal-weight combinations.

Technology Category

• Reasoning under Uncertainty: Stochastic Optimization
• Search and Optimization: Metareasoning and Metaheuristics
• Machine Learning: Ensemble Methods

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

This paper proposes corrected forecast combinations when the original combined forecast errors are serially dependent. Motivated by the classic Bates and Granger (1969) example, we show that combined forecast errors can be strongly autocorrelated and that a simple correction--adding a fraction of the previous combined error to the next-period combined forecast--can deliver sizable improvements in forecast accuracy, often exceeding the original gains from combining. We formalize the approach within the conditional risk framework of Gibbs and Vasnev (2024), in which the combined error decomposes into a predictable component (measurable at the forecast origin) and an innovation. We then link this correction to efficient estimation of combination weights under time-series dependence via GLS, allowing joint estimation of weights and an error-covariance structure. Using the U.S. Survey of Professional Forecasters for major macroeconomic indices across various subsamples (including pre and post-2000, GFC, and COVID), we find that a parsimonious correction of the mean forecast with a coefficient around 0.5 is a robust starting point and often yields material improvements in forecast accuracy. For optimal-weight forecasts, the correction substantially mitigates the forecast combination puzzle by turning poorly performing out-of-sample optimal-weight combinations into competitive forecasts.

Problem

• forecast combinations
• serial dependence
• forecast error autocorrelation
• combination weights
• forecast accuracy

Innovation

• corrected forecast combinations
• serially dependent errors
• forecast combination puzzle
• GLS estimation
• conditional risk framework