Prediction Intervals for a Noisy Nonlinear Time Series Based on a Bootstrapping Reservoir Computing Network Ensemble

Prediction intervals that provide estimated values as well as the corresponding reliability are applied to nonlinear time series forecast. However, constructing reliable prediction intervals for noisy time series is still a challenge. In this paper, a bootstrapping reservoir computing network ensemble (BRCNE) is proposed and a simultaneous training method based on Bayesian linear regression is developed. In addition, the structural parameters of the BRCNE, that is, the number of reservoir computing networks and the reservoir dimension, are determined off-line by the 0.632 bootstrap cross-validation. To verify the effectiveness of the proposed method, two kinds of time series data, including the multisuperimposed oscillator problem with additive noises and a practical gas flow in steel industry are employed here. The experimental results indicate that the proposed approach has a satisfactory performance on prediction intervals for practical applications.