This paper investigates the performance of Echo State Networks (ESNs) for univariate time series forecasting using a subset of the M4 Forecasting Competition dataset. Focusing on monthly and quarterly time series, we evaluate whether a simple autoregressive ESN can serve as a competitive alternative to widely used forecasting methods. The study adopts a two-stage approach: a *Parameter* dataset is used to conduct an extensive hyperparameter sweep covering leakage rate, spectral radius, reservoir size, and information criteria for regularization, resulting in over four million ESN model fits; a disjoint *Forecast* dataset is then used for out-of-sample accuracy assessment. Forecast accuracy is measured using mean absolute scaled error (MASE) and symmetric mean absolute percentage error (sMAPE) and benchmarked against simple benchmarks like drift and seasonal naive and statistical models like autoregressive integrated moving average (ARIMA), exponential smoothing state space (ETS), the Theta method, and TBATS (trigonometric, Box-Cox transformation, ARMA errors, trend, and seasonal components). The hyperparameter analysis reveals broadly consistent and interpretable patterns, with monthly series favoring moderately persistent reservoirs and quarterly series favoring more contractive dynamics. Across both frequencies, high leakage rates are preferred, while optimal spectral radii and reservoir sizes vary with frequency. In the out-of-sample benchmarking, the ESN performs on par with ARIMA and TBATS for monthly data and achieves the lowest mean MASE for quarterly data, while requiring lower computational cost than ARIMA and TBATS. Overall, the results demonstrate that ESNs offer a balance between forecast accuracy, robustness, and computational efficiency, positioning them as a practical option for time series forecasting.

翻译：本文研究了回声状态网络（Echo State Networks, ESNs）在M4预测竞赛数据子集上对单变量时间序列预测的性能。聚焦于月度与季度时间序列，我们评估了简单的自回归回声状态网络是否能够作为广泛使用的预测方法的竞争性替代方案。研究采用两阶段方法：使用*参数*数据集进行广泛的超参数扫描，涵盖泄漏率、谱半径、储层规模及正则化的信息准则，共完成超过四百万个ESN模型拟合；随后使用独立的*预测*数据集进行样本外精度评估。预测精度通过平均绝对缩放误差（MASE）和对称平均绝对百分比误差（sMAPE）衡量，并与简单基准模型（如漂移模型和季节朴素模型）及统计模型（如自回归积分滑动平均模型（ARIMA）、指数平滑状态空间模型（ETS）、Theta方法、TBATS（三角变换、Box-Cox变换、ARMA误差、趋势与季节成分））进行对比。超参数分析揭示了广泛一致且可解释的模式：月度序列偏好中等持久性的储层，而季度序列偏好更具收缩性的动态。在两种频率下，高泄漏率均被优先选择，而最优谱半径与储层规模随频率变化。在样本外基准测试中，ESN在月度数据上表现与ARIMA和TBATS相当，并在季度数据上实现了最低的平均MASE，同时计算成本低于ARIMA和TBATS。总体而言，结果表明ESN在预测精度、鲁棒性和计算效率之间取得了平衡，使其成为时间序列预测的实用选择。