A secondary decomposition-ensemble framework for interval carbon price forecasting

To enhance the accuracy of interval carbon price forecasting, this study proposes a secondary decomposition-ensemble framework. Firstly, the bivariate empirical mode decomposition (BEMD) is applied for primary decomposition of the original interval-valued time series (ITS). Next, the multi-scale permutation entropy (MPE) is introduced to measure the unpredictability of each decomposed component ITS, and the multivariate variational mode decomposition (MVMD) is employed to implement secondary decomposition of the component ITS with the highest complexity. Then, a sparrow search algorithm-enhanced interval multi-layer perceptron (SSA-iMLP) is developed for forecasting each component ITS. Finally, all forecasts of component ITSs are aggregated into ITS forecasts of carbon prices. Using carbon price ITS data from Hubei and Guangdong Emission Exchanges in China, empirical analysis is conducted. The results show that our proposed model has higher predictive accuracy and stronger robustness than benchmark models, indicating that the framework is promising for ITS forecasting in complex scenarios.