Title: Benchmarking and Hyperparameter Optimization of Echo State Networks in Time Series Prediction

Abstract

This study assesses the efficacy of Echo State Networks (ESNs) in generating univariate forecasts for monthly and quarterly time series drawn from the M4 Forecasting Competition dataset. Specifically, we examine whether a straightforward first-order autoregressive ESN can function as a robust competitor to established forecasting techniques. The research employs a two-phase methodology: first, a Parameter dataset is utilized to investigate the impact of various ESN configurations, focusing on leakage rate, spectral radius, reservoir size, and regularization selection. Second, a separate Forecast dataset is designated for out-of-sample benchmarking.

Forecast precision is quantified using the mean absolute scaled error (MASE) and symmetric mean absolute percentage error (sMAPE). These metrics are compared against several baseline and statistical models, including the Theta method, exponential smoothing state space (ETS), autoregressive integrated moving average (ARIMA), and TBATS. Our analysis of model configurations uncovers patterns specific to data frequency: monthly series generally perform better with moderately persistent reservoirs, while quarterly series benefit from more contractive dynamics. Regardless of frequency, high leakage rates are consistently preferred.

In the final benchmarking phase, the ESN demonstrates performance comparable to ARIMA and TBATS for monthly data and records the lowest mean MASE for quarterly data, though it does not dominate across every metric. The findings suggest that a simple autoregressive ESN offers competitive forecast accuracy on the filtered M4 subsets, particularly when evaluated by MASE. Furthermore, once the ESN configuration is established, the model demands minimal time for both training and forecasting.

Source: arXiv Generated at: 2026-06-02 00:00:00 UTC