RF-LSTM carbon price prediction based on CEEMDAN decomposition and multiscale entropy reconstruction

In view of the increasing volatility and complexity of carbon trading markets, accurate forecasting models are essential for policy formulation and risk management. This paper proposed an RF-LSTM hybrid prediction model based on CEEMDAN decomposition and multiscale entropy reconstruction. The model incorporates a rolling decomposition–prediction framework to address the nonlinear and non-stationary characteristics of the carbon market. First, the dataset is divided, and the training set is used as the initial rolling window. Within each window, CEEMDAN decomposes the carbon price series into multiple intrinsic mode functions (IMFs). These IMFs are then grouped according to their similarity in multiscale entropy. The grouped high-frequency components are predicted using the RF model, while the remaining components are modeled by LSTM networks. The prediction results are then integrated to forecast the next data point. After each prediction step, the training window moves forward, and the entire process of decomposition, reconstruction, and prediction is repeated until the end of the series. Experiments using Hubei and European Union data demonstrate the superior accuracy and stability of the proposed model. In addition, a composite score metric, combining model error and runtime, is introduced to provide a balanced evaluation of forecasting performance.