Effect of time scale on chaotic time series prediction using echo state network

Abstract

Echo state networks (ESNs) can achieve high prediction accuracy for time series; however, their performance is highly sensitive to the choice of hyperparameters. Although the hyperparameter selection depends on the characteristics of target systems, especially the autocorrelation structure of time series, the relationship between the hyperparameter selection and the characteristics of target systems remains unclear. Therefore, in this paper, we adjust the time scale of the target time series to clarify the relationship between their autocorrelation structure and suitable hyperparameters of ESNs in prediction tasks. We modify the time scale while preserving essential dynamics by introducing the concept of decorrelation time. In numerical experiments, we performed predictions using an ESN for three chaotic time series with adjusted time scales to investigate the effects of the time scale on the hyperparameter selection in ESNs. The results show that by the adjustment to the same time scale of the time series, parameter regions with high prediction accuracy exhibit similar structures regardless of the target time series. In particular, when predicting time series of longer time scales, high prediction accuracy was obtained in the range in which the spectral radius exceeds unity. These results emphasize the importance of determining the hyperparameters of ESNs based on the time scale of the target time series and provide universal guidelines to select the hyperparameters of ESNs.