Abstract
This paper explores the use of Echo State Networks (ESNs) for univariate time series forecasting, focusing on monthly and quarterly data from the M4 Forecasting Competition dataset. ESNs, a type of reservoir computing model, offer a balance between computational efficiency and predictive accuracy by using a fixed, randomly initialized reservoir and training only a linear readout layer. The study conducts a large-scale hyperparameter sweep, evaluating over four million ESN configurations to optimize parameters such as leakage rate, spectral radius, reservoir size, and regularization criteria. Forecast accuracy is assessed using MASE and sMAPE metrics and benchmarked against statistical models like ARIMA, ETS, and TBATS, as well as naive methods. Results show that ESNs perform competitively, achieving the lowest mean MASE for quarterly data and comparable accuracy to ARIMA and TBATS for monthly data, while requiring less computational effort. The findings highlight ESNs as a robust and scalable option for automated time series forecasting, particularly in scenarios with limited historical data.
Methodology
The study employs a two-stage evaluation approach. First, a hyperparameter sweep is conducted on a Parameter dataset to optimize ESN configurations, including leakage rate, spectral radius, reservoir size, and regularization criteria. Second, out-of-sample forecasting accuracy is assessed on a disjoint Forecast dataset using standardized metrics (MASE and sMAPE). Preprocessing steps include stationarity testing, differencing, and scaling. Forecasts are generated recursively over standard M4 horizons (18 months for monthly data and 8 quarters for quarterly data). ESN performance is benchmarked against naive methods and statistical models like ARIMA, ETS, and TBATS.
Results
The hyperparameter sweep reveals that monthly series favor moderately persistent reservoirs, while quarterly series prefer more contractive dynamics. High leakage rates are optimal across both frequencies, with spectral radii and reservoir sizes varying by temporal resolution. In out-of-sample evaluations, ESNs perform on par with ARIMA and TBATS for monthly data and achieve the lowest mean MASE for quarterly data. ESNs also demonstrate lower computational costs compared to complex statistical models.
Implications
The findings position Echo State Networks as a viable alternative to traditional statistical methods for automated time series forecasting, particularly in business and economic applications with short historical data. Their computational efficiency and robustness make them suitable for large-scale forecasting tasks, addressing the growing demand for scalable and automated solutions in data-driven decision-making.
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