An innovative random forest-based nonlinear ensemble paradigm of improved feature extraction and deep learning for carbon price forecasting.

Carbon price is the basis of developing a low carbon economy. The accurate carbon price forecast can not only stimulate the actions of enterprises and families, but also encourage the study and development of low carbon technology. However, as the original carbon price series is non-stationary and nonlinear, traditional methods are less robust to predict it. In this study, an innovative nonlinear ensemble paradigm of improved feature extraction and deep learning algorithm is proposed for carbon price forecasting, which includes complete ensemble empirical mode decomposition (CEEMDAN), sample entropy (SE), long short-term memory (LSTM) and random forest (RF). As the core of the proposed model, LSTM enhanced from the recurrent neural network is utilized to establish appropriate prediction models by extracting memory features of the long and short term. Improved feature extraction, as assistant data preprocessing, represents its unique advantage for improving calculating efficiency and accuracy. Removing irrelevant features from original time series through CEEMDAN lets learning easier and it's even better for using SE to recombine similar-complexity modes. Furthermore, compared with simple linear ensemble learning, RF increases the generalization ability for robustness to achieve the final nonlinear output results. Two markets' real data of carbon trading in china are as the experiment cases to test the effectiveness of the above model. The final simulation results indicate that the proposed model performs better than the other four benchmark methods reflected by the smaller statistical errors. Overall, the developed approach provides an effective method for predicting carbon price.