Enhanced multi-step streamflow series forecasting using hybrid signal decomposition and optimized reservoir computing models

This study evaluates the use of different time series decomposition methods in association with echo state networks (ESNs), deep echo state networks (DeepESNs), and next generation reservoir computing (NGRC) models to predict the natural flow of water in two hydropower reservoirs with horizons of one, seven, fourteen, and twenty-one steps ahead. The Coyote optimization algorithm is used to adjust the hyperparameters of the ESNs. The use of reservoir computing (RC) methods with Coyote optimization algorithm, a swarm intelligence approach, is compared with the use of variational mode decomposition (VMD), empirical wavelet transform, and empirical mode decomposition. Analysis of the results shows that the use of signal decomposition methods in association with RC can improve the accuracy and performance of the prediction model. The results are compared using different statistical metrics, showing that, in most cases, decomposition methods can improve the forecasting performance of RC. Overall, NGRC outperformed ESN and DeepESN in most of evaluated cases. The best results were obtained using VMD for the forecast horizons of 7, 14, and 21 days ahead, with a decrease in mean absolute error in a range from 43.70% to 88.88% compared to all the other models. Using a Diebold–Mariano test, the results show that the use of VMD is statistically significant in all the cases, with a significant value of 1% in all tested cases of ESN forecasting.