Multi-step carbon price forecasting based on a new quadratic decomposition ensemble learning approach

Numerous studies show that it is reasonable and effective to apply decomposition technology to deal with the complex carbon price series. However, the existing research ignores the residual term containing complex information after applying single decomposition technique. Considering the demand for higher accuracy of the carbon price series prediction and following the existing research path, this paper proposes a new hybrid prediction model VMD-CEEMDAN-LSSVM-LSTM, which combines a new quadratic decomposition technique with the optimized long short term memory (LSTM). In the decomposition part of the hybrid model, the original carbon price series is processed by variational mode decomposition (VMD), and then the residual term obtained by decomposition is further decomposed by complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN). In the prediction part of the hybrid model, least squares support vector machine (LSSVM) is introduced, and LSSVM-LSTM model is constructed to predict the components obtained by decomposition. The empirical research of this paper selects two different case data from the European Union emissions trading system (EU ETS) as samples. Taking the results of Case Ⅰ in the 1-step ahead forecasting scenario as an example, the prediction evaluation indexes