Giovanni Ballarin, Lyudmila Grigoryeva, Yui Ching Li
arXiv 15 Dec 2025 · Econometrics
arXiv:2512.13642 · PDF · DOI · OpenAlex · Extracted main text
Model combination is a powerful approach for achieving superior performance compared to selecting a single model. We study both theoretically and empirically the effectiveness of ensembles of Multi-Frequency Echo State Networks (MFESNs), which have been shown to achieve state-of-the-art macroeconomic time series forecasting results (Ballarin et al., 2024a). The Hedge and Follow-the-Leader schemes are discussed, and their online learning guarantees are extended to settings with dependent data. In empirical applications, the proposed Ensemble Echo State Networks demonstrate significantly improved predictive performance relative to individual MFESN models.
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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 | Littlestone, N. and Warmuth, M. K (1994) The weighted majority algorithm | 1.000 | 5 | 3 | 100% |
| 2 | de Rooij, S., van Erven, T., Grünwald, P. D., and Koolen, W. M (2014) Follow the Leader if you can, Hedge if you must | 0.969 | 11 | 4 | 91% |
| 3 | Cesa-Bianchi, N. and Lugosi, G (2006) Prediction, Learning, and Games | 0.928 | 5 | 3 | 80% |
| 4 | van Erven, T., Koolen, W. M., de Rooij, S., and Grünwald, P (2011) Adaptive Hedge | 0.874 | 5 | 2 | 100% |
| 5 | Ballarin, G., Dellaportas, P., Grigoryeva, L., Hirt, M., van Huellen… (2024) Reservoir Computing for macroeconomic forecasting with mixed frequency data self | 0.849 | 31 | 7 | 61% |
| 6 | Timmermann, A (2006) Chapter 4 Forecast Combinations | 0.843 | 4 | 3 | 75% |
| 7 | Mourtada, J. and Gaïffas, S (2019) On the optimality of the Hedge algorithm in the stochastic regime | 0.737 | 15 | 5 | 40% |
| 8 | Chernov, A. and Zhdanov, F (2010) Prediction with Expert Advice under Discounted Loss | 0.737 | 4 | 3 | 50% |
| 9 | Freund, Y. and Schapire, R. E (1997) A decision-theoretic generalization of online learning and an application to boosting | 0.737 | 3 | 2 | 100% |
| 10 | Bates, J. M. and Granger, C (1969) The combination of forecasts | 0.644 | 2 | 2 | 100% |
Showing the top 10 of 82 scored citations.