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.

翻译：模型集成是一种强大的方法，其性能通常优于选择单一模型。我们从理论和实证两方面研究了多频率回声状态网络（MFESN）集成的有效性，该网络已被证明能够实现最先进的宏观经济时间序列预测结果（Ballarin 等人，2024a）。本文讨论了 Hedge 和 Follow-the-Leader 方案，并将其在线学习保证扩展到具有依赖数据的场景中。在实证应用中，所提出的集成回声状态网络相较于单个 MFESN 模型，展现出显著提升的预测性能。