Accurately predicting the price of carbon is an effective way of ensuring the stability of the carbon trading market and reducing carbon emissions. Aiming at the non-smooth and non-linear characteristics of carbon price, this paper proposes a novel hybrid prediction model based on improved feature extraction and non-linear integration, which is built on complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN), fuzzy entropy (FuzzyEn), improved random forest using particle swarm optimisation (PSORF), extreme learning machine (ELM), long short-term memory (LSTM), non-linear integration based on multiple linear regression (MLR) and random forest (MLRRF), and error correction with the autoregressive integrated moving average model (ARIMA), named CEEMDAN-FuzzyEn-PSORF-ELM-LSTM-MLRRF-ARIMA. Firstly, CEEMDAN is combined with FuzzyEn in the feature selection process to improve extraction efficiency and reliability. Secondly, at the critical prediction stage, PSORF, ELM, and LSTM are selected to predict high, medium, and low complexity sequences, respectively. Thirdly, the reconstructed sequences are assembled by applying MLRRF, which can effectively improve the prediction accuracy and generalisation ability. Finally, error correction is conducted using ARIMA to obtain the final forecasting results, and the Diebold–Mariano test (DM test) is introduced for a comprehensive evaluation of the models. With respect to carbon prices in the pilot regions of Shenzhen and Hubei, the results indicate that the proposed model has higher prediction accuracy and robustness. The main contributions of this paper are the improved feature extraction and the innovative combination of multiple linear regression and random forests into a non-linear integrated framework for carbon price forecasting. However, further optimisation is still a work in progress.

Comprehensively clarifying the influencing factors of carbon emissions is crucial to realizing carbon emission reduction targets in China. To address this issue, this paper develops a four-level carbon emission influencing factor system from six perspectives: population, economy, energy, water resources, main pollutants, and afforestation. To analyze how these factors affect carbon emissions, we propose an improved partial least squares structural equation model (PLS-SEM) based on a random forest (RF), named RF-PLS-SEM. In addition, the entropy weight method (EWM) is employed to evaluate the low-carbon development level according to the results of the RF-PLS-SEM. This paper takes Shandong Province as an example for empirical analysis. The results demonstrate that the improved model significantly improves accuracy from 0.8141 to 0.9220. Moreover, water resources and afforestation have relatively small impacts on carbon emissions. Primary and tertiary industries are negative influencing factors that inhibit the growth of carbon emissions, whereas total energy consumption, the volume of wastewater discharged and of common industrial solid waste are positive and direct influencing factors, and population density is indirect. In particular, this paper explores the important role of fisheries in reducing carbon emissions and discusses the relationship between population aging and carbon emissions. In terms of the level of low-carbon development, the assessment system of carbon emission is constructed from four dimensions, namely, population, economy, energy, and main pollutants, showing weak, basic, and sustainable stages of low-carbon development during the 1997–2012, 2013–2020, and 2021–2022 periods, respectively.

Accurate carbon price forecasting is essential for market stability, risk management, and policy-making. To address the nonlinear, non-stationary, and multiscale nature of carbon prices, this paper proposes a forecasting framework integrating secondary decomposition, two-stage feature selection, and dynamic ensemble learning. Firstly, the original price series is decomposed into intrinsic mode functions (IMFs), using complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN). The IMFs are then grouped into low- and high-frequency components based on multiscale entropy (MSE) and K-Means clustering. To further alleviate mode mixing in the high-frequency components, an improved variational mode decomposition (VMD) optimized by particle swarm optimization (PSO) is applied for secondary decomposition. Secondly, a two-stage feature-selection method is employed, in which the partial autocorrelation function (PACF) is used to select relevant lagged features, while the maximal information coefficient (MIC) is applied to identify key variables from both historical and external data. Finally, this paper introduces a dynamic integration module based on sliding windows and sequential least squares programming (SLSQP), which can not only adaptively adjust the weights of four base learners but can also effectively leverage the complementary advantages of each model and track the dynamic trends of carbon prices. The empirical results of the carbon markets in Hubei and Guangdong indicate that the proposed method outperforms the benchmark model in terms of prediction accuracy and robustness, and the method has been tested by Diebold Mariano (DM). The main contributions are the improved feature-extraction process and the innovative use of a sliding window-based SLSQP method for dynamic ensemble weight optimization.