A Gaussian process echo state networks model for time series forecasting

In this paper, a novel Gaussian process echo state networks (GPESN) model is proposed for time series forecasting. This method establishes the direct relationship between the prediction origin and prediction horizon without iterating in the prediction process, which avoids the accumulative iteration error. Instead of using linear regression, Gaussian process is used to obtain the relationship between the reservoir state and network output of ESN, which eliminates the ill conditioned reservoir state matrix. The GPESN model is capable of achieving not only a better prediction result but also an accurate probability estimation of the results. The proposed method is verified by the standard prediction benchmark, Mackey-Glass time series, and is applied to a practical prediction problem in steel industry. The experiment results indicate that the proposed GPESN is effective and reliable.