Multi-step carbon price forecasting using a hybrid model based on multivariate decomposition strategy and deep learning algorithms

Accurate prediction of carbon price effectively ensures the stability of the carbon trading market and reduces carbon emissions. However, making accurate prediction is challenging because the carbon price is highly nonlinear and nonstationary due to complex influential factors. Thus, we propose a multifactorial hybrid forecasting framework, ET-MVMD-LSTM, to integrate three advanced algorithms for a reliable multi-step ahead prediction of the carbon price. First, extremely randomized tree (ET) is used to determine the optimal input variables for the modeling to follow. Then, multivariate variational mode decomposition (MVMD) is executed to simultaneously decompose the screened input variables into relatively regular sub-modes, which reflect characteristics at different scales. Subsequently, long short-term memory (LSTM) with a stable forecasting ability is employed to model each mode individually to effectively extract the long-term trend and short-term fluctuation features. The final forecast is reconstructed by the ensemble of the predictions of all sub-modes. Last, systematical studies on two European Union Emissions Trading Scheme carbon price datasets indicate that the proposed ET-MVMD-LSTM framework outperforms several advanced baseline models in terms of accuracy and stability, which prove the framework is deemed promising and practical for carbon price prediction.