An optimized decomposition integration framework for carbon price prediction based on multi-factor two-stage feature dimension reduction

The carbon trading market is an effective tool to combat greenhouse gas emissions, and as the core issue of carbon market, carbon price can stimulate the market for technological innovation and industrial transformation. However, the complex characteristics of carbon price such as nonlinearity and nonstationarity bring great challenges to carbon price prediction research. In this study, potential influencing factors of carbon price are introduced into carbon price forecasting, and a novel hybrid carbon price forecasting framework is developed, which contains data decomposition and reconstruction techniques, two-stage feature dimension reduction methods, intelligent and optimized deep learning forecasting with nonlinear integrated models and interval forecasting. Firstly, the carbon price series is decomposed into several simple and smooth subsequences using variational modal decomposition. The stacked autoencoder is then used to extract its effective features and reconstruct them into several new subsequences. A two-stage feature dimension reduction method is utilized for feature selection and extraction of exogenous variables. A bidirectional long and short-term memory model optimized based on the cuckoo search algorithm was used for prediction and nonlinear integration. Finally, Gaussian process regression based on a hybrid kernel function is applied to carbon price interval forecasting. The validity of the model was verified on seven real carbon trading pilot datasets in China. The methodology outperforms all benchmark models in the final simulation results, providing a novel and efficient forecasting method for the carbon trading industry.