arXiv 15 Jan 2026 · Econometrics
arXiv:2601.09999 · PDF · DOI · OpenAlex · Extracted main text
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.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Christopher G. Gibbs and Vasnev, Andrey L (2024) Conditionally optimal weights and forward-looking approaches to combining forecasts self | 1.000 | 9 | 5 | 100% |
| 2 | Bates, J. M. and Granger, C. W. J (1969) The combination of forecasts | 1.000 | 8 | 5 | 100% |
| 3 | Granger, Clive W J and Ramanathan, Ramu (1984) Improved methods of combining forecasts | 0.843 | 3 | 3 | 100% |
| 4 | Xiaoqian Wang and Rob J. Hyndman and Feng Li and Yanfei Kang (2023) Forecast combinations: An over 50-year review | 0.737 | 3 | 2 | 100% |
| 5 | Satyanarayana Poojari and Sachin Acharya and Varun Kumar S.G. and Vi… (2025) Modified least squares ratio estimator for autocorrelated data: Estimation and prediction | 0.644 | 2 | 2 | 100% |
| 6 | Gerda Claeskens and Jan R. Magnus and Andrey L. Vasnev and Wendun Wang (2016) The forecast combination puzzle: A simple theoretical explanation self | 0.644 | 2 | 2 | 100% |
| 7 | Barnard, G. A (1963) New Methods of Quality Control | 0.405 | 1 | 1 | 100% |
| 8 | Raffaella Giacomini and Halbert White (2006) Tests of conditional predictive ability | 0.405 | 1 | 1 | 100% |
| 9 | Rob J. Hyndman and Bahman Rostami-Tabar (2025) Forecasting interrupted time series | 0.405 | 1 | 1 | 100% |
| 10 | Stock, J. H. and Watson, M. W (2004) Combination forecasts of output growth in a seven-country data set | 0.405 | 1 | 1 | 100% |
Showing the top 10 of 15 scored citations.