Time series forecasting based on echo state network and empirical wavelet transformation

Echo state network (ESN) is a reservoir computing structure consisting randomly generated hidden layer which enables a rapid learning and extrapolation process. On the other hand, the determination of inputs is still an outstanding question similar to other neural networks. Instead of utilizing the original historical data, wavelet transformations can be used to extract and reflect features with predictability (periodicity) and eliminate random oscillations (i.e. noise) which would distort the underlying predictive structure. In this regard, we propose a two-stage predictive algorithm in which the empirical wavelet transformation (EWT) has been implemented to transform the data, and ESN is utilized to execute the overall predictive process. The proposed method has been validated by twelve public datasets with different mean-volatility features. Out of sample forecasts have been compared to the baseline persistence model and conventional benchmarks. The empirical study demonstrates the superiority of the EWT–ESN model compared with other models.