Time series forecasting by the novel Gaussian process wavelet self-join adjacent-feedback loop reservoir model

Abstract

For a long time, echo state network (ESN) has been a good application in solving the time series forecasting problem. As an improved ESN, the Self-join Adjacent-feedback Loop Reservoir (SALR) model effectively solves the problem for which ESN is not principled enough and its computational cost is too large. On this basis, this study proposes a novel Gaussian Process Wavelet Self-join Adjacent-feedback Loop Reservoir (GP-WSALR) model. It combines the advantages of SALR and Gaussian process regression, and provides a more reliable alternative than the traditional reservoir calculation model. At the same time, by adjusting the neurons in the reservoir, the problem of poor nonlinear approximation ability and easily fall into singular solutions caused by a single S-type neurons is solved. Specifically, this study proposes to: (1) use Gaussian process regression to replace the classic linear regression method to obtain the output weight of SALR and (2) use wavelet neurons to replace part of the S-type neurons in the GP-SALR reservoir. The novel Gaussian Process Wavelet Self-join Adjacent-feedback Loop Reservoir (GP-WSALR) model is developed by the two new mechanisms. The experimental results show that GP-WSALR obtains superior forecasting accuracy in the electrical load and network traffic forecasting problems.