Carbon price forecasting using leaky integrator echo state networks with the framework of decomposition-reconstruction-integration

Carbon trading is one of the strategies to achieve the goal of dual carbon. However, carbon prices exhibit non-stationary and nonlinear characteristics, posing significant challenges for accurate forecasting. Inspired by the ideas of “division and conquest” and “granularity reconstruction”, a decomposition-reconstruction-integration framework is built for carbon price forecasting. The proposed model leverages a comprehensive ensemble empirical mode decomposition with adaptive noise (CEEMDAN) and sample entropy (SE) to extract features from two perspectives of time and complexity, and thus the one-dimensional time series of carbon price is reconstructed into different items. Subsequently, leaky integrator echo state networks (LiESNs) are utilized to forecast each of these items individually. These individual forecasts are then integrated to generate the final point forecast. To evaluate the uncertainty of the point forecast, a Gaussian process model is applied to interval forecast. The proposed model comprehensively considers the time series features of carbon price including the temporal modal features in the decomposition stage, the entropy probability features in the reconstruction stage, and the essential temporal dependencies via dynamic reservoir of interconnected neurons in the integration forecasting stage. Experimental results demonstrate the model's exceptional forecasting performance, surpassing the effectiveness of alternative approaches.