| Summary: | Effective forecasting of carbon prices helps investors to judge carbon market conditions and promotes the environment and economic sustainability. The contribution of this paper is constructing a novel secondary decomposition hybrid carbon price forecasting model, namely CEEMD-SE-VMD-LSTM. It is noteworthy that the sample entropy is introduced to identify the highly complex signals rather than empirically determined in previous studies. Specifically, the complementary ensemble empirical mode decomposition (CEEMD) model is used to decompose the original price signals. The sample entropy (SE) and variational mode decomposition (VMD) are conducted to recognize and secondary decompose the highly complex components, while the long short-term memory (LSTM) model is employed to forecast the carbon price by summing up the predicted intrinsic mode function (IMF) components. The conclusion shows the proposed model has the smallest forecasting errors with the values of RMSE, MAE and MAPE are 0.2640, 0.1984 and 0.0044, respectively, the secondary decomposition models are better than other primary decomposition models and the forecasting performances of LSTM-type models are better than those of other GRU-type models. Further evidence convinces us that short-term forecasting accuracy is superior to long-term forecasting. Those conclusions and model innovation can provide a valuable reference for investors to make trading decisions.
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