Carbon Price Series Research Articles

A dual decomposition integration and error correction model for carbon price prediction.

Accurately predicting carbon prices is crucial for effective government decision-making and maintenance the stable operation of carbon markets. However, the instability and nonlinearity of carbon prices, driven by the complex interaction between economic, environmental, and political factors, often result in inaccurate predictions. To confront this challenge, this paper proposed a carbon price prediction model that integrates dual decomposition integration and error correction. Firstly, the variational mode decomposition optimized by the sparrow search algorithm (SVMD) is used to decompose carbon price series into intrinsic mode functions (IMFs). Secondly, a classification-prediction module is constructed to classify IMFs on complexity using fuzzy entropy. The long short-term memory networks optimized by the whale optimization algorithm (WLSTM) is employed to capture temporal dynamics and long-term dependencies within data. Conversely, lower complexity IMFs characterized by smoother trends and less erratic behavior are predicted using computationally efficient extreme learning machines (ELM). To further refine the prediction accuracy, ensemble empirical mode decomposition (EEMD) is introduced to decompose the initially predicted error series into IMFs and then predicted by classification-prediction module. Reconstruct the initial prediction IMFs and the error prediction IMFs to obtain the final prediction results. Finally, the proposed model was validated using real carbon price data from three Chinese carbon exchanges. Compared with the 15 comparison models, the performance indicators RMSE, MAE, MAPE, and R2 of the proposed model have promoted at least 19.89%, 25.11%, 25.01%, and 0.79% on average. These results underscore the effectiveness and superiority in predicting carbon prices, providing a robust tool for carbon market stakeholders and climate change policymakers.

Integrating fast iterative filtering and ensemble neural network structure with attention mechanism for carbon price forecasting

Accurate carbon price forecasts are crucial for policymakers and enterprises to understand the dynamics of carbon price fluctuations, enabling them to formulate informed policies and investment strategies. However, due to the non-linear and non-stationary nature of carbon price, traditional models often struggle to achieve high prediction accuracy. To address this challenge, this study proposes a novel integrated prediction framework designed to enhance forecast accuracy. First, the carbon price series is decomposed into a series of smoother subsequences using fast iterative filtering (FIF). Subsequently, an integrated prediction model, AM-TCN-LSTM, is constructed, incorporating the attention mechanism (AM), temporal convolutional networks (TCN), and long short-term memory (LSTM) neural networks. The attention mechanism adaptively captures complex features from multiple factors, while the TCN-LSTM efficiently extracts temporal features from the sequences. Finally, the results from each subsequence are aggregated to generate the final prediction. Five carbon markets in china: Guangdong, Hubei, Shenzhen, Beijing, and Shanghai were selected to verify the validity of the proposed model. Various comparative models and evaluation metrics were employed to assess performance. The results demonstrate that: (1) the TCN-LSTM model achieves higher prediction accuracy compared to single models. (2) FIF is a more effective decomposition method with superior performance compared to EMD-based methods. (3) The proposed model exhibits the highest predictive capability, with MAE values of 0.0964, 0.1403, 1.9476, 2.0848, and 0.5029 for the five carbon markets, significantly outperforming comparison models. (4) The attention mechanism effectively captures the influence of multiple factors on carbon price, particularly within the short-term components.

A Sustainable Model for Forecasting Carbon Emission Trading Prices

Carbon trading has garnered considerable attention as a pivotal policy instrument for advancing carbon peaking and carbon neutrality, which are essential components of sustainable development. The capacity to precisely anticipate the cost of carbon trading has significant implications for the optimal deployment of market mechanisms, the economic advancement of technological innovations in corporate emissions reduction, and the facilitation of international energy policy adjustments. To this end, this paper proposes a novel and sustainable trading price prediction tool that employs a four-step process: decomposition, reconstruction, prediction, and integration. This innovative approach first utilizes the Improved Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (ICEEMDAN), then reconstructs the decomposition set using multi-scale entropy (MSE), and finally uses the Long Short-Term Memory neural network model (LSTM) enhanced by the Grey Wolf Optimizer (GWO) to predict the carbon emission trading price. The experimental results demonstrate that the tool achieves high accuracy for both the EU carbon price series and the carbon price series of China’s seven major carbon trading markets, with accuracy rates of 99.10% and 99.60% in Hubei and the EU carbon trading markets, respectively. This represents an improvement of approximately 3.1% over the ICEEMDAN-LSTM model and 0.91% over the ICEEMDAN-MSE-LSTM model, thereby contributing to more sustainable and efficient carbon trading practices.

Framework for multivariate carbon price forecasting: A novel hybrid model

The complex characteristics of volatility and non-linearity of carbon price pose a serious challenge to accurately predict carbon price. Therefore, this study proposes a new hybrid model for multivariate carbon price forecasting, including feature selection, deep learning, intelligent optimization algorithms, model combination and evaluation indicators. First, this study collects and organizes the historical carbon price series of Hubei and Shanghai as well as the influencing factors in five dimensions including structured and unstructured data, totaling twenty variables. Second, data dimensionality reduction is performed and input variables are obtained using the least absolute shrinkage and selection operator, followed by the introduction of nine advanced deep learning models to predict carbon price and compare the prediction effects. Then, through the combination of models, three models with the best performance are combined with Pelican optimization algorithm to construct a hybrid forecasting model. Finally, the experimental results show that the developed forecasting model outperforms other comparation models in terms of prediction accuracy, stability and statistical hypothesis testing, and exhibits excellent prediction performance. Furthermore, this study also applies the developed model to European carbon market price prediction and uses the Hubei carbon market as an example for quantitative trading simulation, and the empirical results further verify its robust prediction performance and investment application value. In conclusion, the proposed hybrid prediction model can not only provide high-precision carbon market price prediction for the government and corporate decision makers, but also help investors optimize their trading strategies and improve their returns.

A combined model based on decomposition and reorganization, weight optimization algorithms for carbon price point and interval prediction

With the increasing environmental and climate problems caused by global warming, more and more countries are paying attention to reducing carbon emissions. Accurately predicting carbon prices can help create a stable carbon market and mitigate global warming. Therefore, a combined model which has four modules is proposed, they are the decomposition of carbon price series, reorganization of subsequences, point forecasting, and interval forecasting. For data preprocessing of decomposition, it can reduce the non-linearity of sequences. Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN) decomposes the original series into multiple Intrinsic Mode Functions (IMFs). Reorganization uses SampEn (SE) and T-test to reorganize the decomposed sequence into three new sequences according to actual meanings. For point prediction, the combined prediction model uses Particle Swarm Optimization (PSO) to obtain the optimal weights of Recurrent Neural Network (RNN), Long Short-Term Memory (LSTM), and Gated Recurrent Unit (GRU), which can integrate their strengths to improve prediction accuracy. Interval prediction is based on fitting the optimal distribution function by Maximum Likelihood Estimate (MLE). Different significance intervals can be obtained from the point prediction results and the distribution function. Empirical and comparative experiments show this combined model has excellent point and interval predictions. Besides, the significance and stability are demonstrated. Finally, some valuable references are provided for policymakers.

A hybrid carbon price prediction model based-combinational estimation strategies of quantile regression and long short-term memory

In recent years, global warming mitigation has received increasing attention. Reasonable carbon prices in stable carbon markets can reduce greenhouse gas emissions. Therefore, to accurately predict carbon prices and describe their fluctuations, a hybrid model was developed based on Complete Empirical Mode Decomposition with Adaptive Noise (CEEMDAN), SampEn (SE), Long Short-Term Memory (LSTM), Quantile regression (QR), and Kernel density estimation (KDE). First, CEEMDAN was used to decompose the original carbon price series into several Intrinsic Mode Functions (IMFs), and the SE of each decomposed series was calculated to reconstruct a new series. The actual influencing factors determine the number of new series. The prediction model, named QRLSTM, combines QR and LSTM to achieve point and interval predictions. Finally, KDE was used to obtain a probabilistic prediction of the daily carbon price. Compared with other methods, the experimental results in Hubei, China, showed that the proposed CEEMDAN-SE-QRLSTM model had the best performance. For point prediction, the MSE, MAE, RMSE, MAPE, and R2 were 0.19, 0.33, 0.43, 0.01, and 91.7%, respectively. In interval prediction, the coverage width criterion (CWC) in the 95%, 90%, and 80% confidence intervals was small, with values of 0.37, 0.32, and 0.27, respectively. In probabilistic prediction, the continuous ranked probability score (CRPS) with 95% confidence was small, with a value of 0.25. In addition, the improvement in point prediction and stability of the hybrid model were also proved. The proposed model can provide more accurate results and valuable information for decision-makers.

Multi-step-ahead and interval carbon price forecasting using transformer-based hybrid model.

Accurate and stable carbon price forecasts serve as a reference for assessing the stability of the carbon market and play a vital role in enhancing investment and operational decisions. However, realizing this goal is still a significant challenge, and researchers usually ignore multi-step-ahead and interval forecasting due to the non-linear and non-stationary characteristics of carbon price series and its complex fluctuation features. In this study, a novel hybrid model for accurately predicting carbon prices is proposed. The proposed model combines multi-step-ahead and interval carbon price forecasting based on the Hampel identifier (HI), time-varying filtering-based empirical mode decomposition (TVFEMD), and transformer model. First, HI identifies and corrects outliers in carbon price. Second, TVFEMD decomposes carbon price into several intrinsic mode functions (imfs) to reduce the non-linear and non-stationarity of carbon price to obtain more regular features in series. Next, these imfs are reconstructed by sample entropy (SE). Subsequently, the orthogonal array tuning method is used to optimize the transformer model's hyperparameters to obtain the optimal model structure. Finally, after hyperparameter optimization and quantile loss function, the transformer is used to perform multi-step-ahead and interval forecasting on each part of the reconstruction, and the final prediction result is obtained by summing them up. Five pilot carbon trading markets in China were selected as experimental objects to verify the proposed model's prediction performance. Various benchmark models and evaluation indicators were selected for comparison and analysis. Experimental results show that the proposed HI-TVFEMD-transformer hybrid model achieves an average MAE of 0.6546, 1.3992, 1.6287, and 2.2601 for one-step, three-step, five-step, and ten-step-ahead forecasting, respectively, which significantly outperforms other models. Furthermore, interval forecasts almost always have a PICI above 0.95 at a confidence interval of 0.1, thereby indicating the effectiveness of the hybrid model in describing the uncertainty in the forecasts. Therefore, the proposed hybrid model is a reliable carbon price forecasting tool that can provide a dependable reference for policymakers and investors.

An ensemble self-learning framework combined with dynamic model selection and divide-conquer strategies for carbon emissions trading price forecasting

A reliable carbon price forecast system is essential for governments to assess “net-zero emission” targets, guiding production, operation, and investment through risk prevention and control measures. Although existing studies report numerous hybrid or ensemble models for carbon price forecasting, there is still considerable room for optimization due to the lack of targeted judgments on series features. This paper proposes a dynamic multi-objective self-learning combination framework based on the model-algorithm space, which adaptively selects the ensemble scheme with the best performance according to the specific laws of the carbon price series features while ensuring the diversity of base models. Furthermore, the developed divide-conquer strategy, which can better quantify signal irregularities, is employed to overcome obstacles caused by the high complexity of some components during data preprocessing. Carbon price series from the European and Shenzhen carbon markets validate the hybrid method's ability to handle different signals. Experimental studies reveal that the proposed carbon price prediction model possesses a reasonable structure and strong interpretability, yielding accurate, robust, and generalized prediction results.

A Multi-Strategy Integration Prediction Model for Carbon Price

Carbon price fluctuations significantly impact the development of industries, energy, agriculture, and stock investments. The carbon price possesses the features of nonlinearity, non-stationarity, and high complexity as a time series. To overcome the negative impact of these characteristics on prediction and to improve the prediction accuracy of carbon price series, a combination prediction model named Lp-CNN-LSTM, which utilizes both convolutional neural networks and long short-term memory networks, has been proposed. Strategy one involved establishing distinct models of CNN-LSTM and LSTM to analyze high-frequency and low-frequency carbon price sequences; the combination of output was integrated to predict carbon prices more precisely. Strategy two comprehensively considered the economic and technical indicators of carbon price sequences based on the Pearson correlation coefficient, while the Multi-CNN-LSTM model selected explanatory variables that strongly correlated with carbon prices. Finally, a predictive model for a combination of carbon prices was developed using Lp-norm. The empirical study focused on China’s major carbon markets, including Hubei, Guangdong, and Shanghai. According to the error indicators, the performance of the Lp-CNN-LSTM model was superior to individual strategy prediction models. The Lp-CNN-LSTM model has excellent accuracy, superiority, and robustness in predicting carbon prices, which can provide a necessary basis for revising carbon pricing strategies, regulating carbon trading markets, and making investment decisions.

Carbon price decomposition ensemble hybrid forecasting model based multi-scale feature extraction

The carbon emission market is the core policy tool to achieve the goal of carbon peaking and carbon neutrality. To fully extract the complex features of carbon price series such as non-stationary, non-linear, and multi-scale etc. This paper constructs an integrated hybrid forecasting model CEEMD-GWO-LSSVR based on the multi-scale decomposition of carbon price decomposition. Firstly, the original carbon price series are decomposed into eigenmodal functions (IMFs) of different scales by complementary ensemble empirical modal decomposition (CEEMD), and the LSSVR model optimized by the grey wolf optimization algorithm (GWO) is used as the prediction model to forecast the obtained IMFs, and finally, the prediction results of all IMFs are linearly integrated. This paper selects the price data of the Shanghai carbon trading market for the empirical study, and the empirical results show that the prediction accuracy of the hybrid model proposed in this paper is significantly better than that of the benchmark model.

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 eMAPE, eRMSE and R2 of the VMD-CEEMDAN-LSSVM-LSTM hybrid model constructed in this paper are 0.3087, 0.0921 and 0.9987 respectively, which are significantly better than other benchmark models. The empirical results confirm the superiority and robustness of the hybrid model proposed in this paper for carbon price forecasting.

An ensemble dynamic self-learning model for multiscale carbon price forecasting

Precise carbon price forecasting can provide decision support for policy-makers and investors. However, due to the high non-stationarity and nonlinearity of carbon price series, it is difficult to get accurate forecasting results under volatile situations. To accommodate different scenarios, this paper proposes a dynamic self-learning integrating forecasting model to forecast the carbon price by considering external impact factors. The multi-dimensional time series is initially decomposed into different intrinsic mode functions simultaneously by the noise-assisted multivariate empirical mode decomposition method. After reconstructing the decomposed series into high-frequency, low-frequency, and trend modules, the extreme learning machine optimized by the cosine-based whale optimization algorithm is proposed to predict the carbon price. The dynamic relationships between the carbon price and impact factors are simulated by the sliding window structure, which improves the adaptability of the proposed model. The high prediction accuracy under different situations including extreme scenarios demonstrates the stability of the proposed model. A self-learning algorithm, which can automatically learn the evolving model structure and update model parameters, is designed to alleviate the underfitting/overfitting problem. The comparison results with existing models indicate the superiority of the proposed model.

Ensemble forecasting system based on decomposition-selection-optimization for point and interval carbon price prediction

In this study, a novel ensemble forecasting system based on data decomposition, feature selection, optimal sub-model determination and the improved multi-objective optimization is designed to conduct both point and interval carbon price predictions. To testify the performance of the developed system, three daily carbon price series are collected for experiments and verification. The results indicated that the ensemble system has achieved the optimal mean absolute percent errors of 0.9267, 1.6433 and 0.9303% for Sites 1–3 during point forecasting. In addition, the prediction interval coverage probabilities of three sites are 0.9800, 0.9600 and 0.9600 under the 95% confidence level for interval forecasting, which demonstrated that the developed system can provide scientific and sufficient reference for carbon trading markets.

Identification of Breakpoints in Carbon Market Based on Probability Density Recurrence Network

The scientific judgement of the structural abrupt transition characteristics of the carbon market price is an important means to comprehensively analyze its fluctuation law and effectively prevent carbon market risks. However, the existing methods for identifying structural changes of the carbon market based on carbon price data mostly regard the carbon price series as a deterministic time series and pay less attention to the uncertainty implied by the carbon price series. We propose a framework for identifying abrupt transitions in the carbon market from the perspective of a complex network by considering the influence of random factors on the carbon price series, expressing the carbon price series as a sequence of probability density functions, using the distribution of probability density to reveal the uncertainty information implied by carbon price series and constructing a recurrence network of carbon price probability density. Based on the community structure, the break index and statistical test method are defined. The simulation verifies the effectiveness and superiority of the method compared with traditional methods. An empirical analysis uses the carbon price data of the European Union carbon market and seven pilot carbon markets in China. The results show many abrupt transitions in the carbon price series of the two markets, whose occurrence period is closely related to major events.

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.

A novel framework for carbon price forecasting with uncertainties

Carbon price prediction is a key issue in the field of carbon market research. However, the existing methods of carbon price forecasting mostly regard carbon price series as a certain time series, but pay less attention to the uncertainty implied by carbon price series. Based on this, this paper proposes a forecasting model framework considering the uncertainty of carbon price series, which represents the carbon price series as a time series of probability density function to deal with the uncertainty. A prediction model based on the probability density recurrence network of carbon price is constructed with the help of the recurrence network construction technology of data and link prediction, and the advantages of the model are verified by numerical simulation. The empirical analysis is made by using the EU carbon price data. In the whole sample interval, we build 123 time windows. The results indicate that our prediction model has better level forecasting precision in 90.69% time windows and directional prediction accuracy in 67.82% time windows than the prediction model built based on deterministic network, which can improve the level prediction accuracy and directional prediction accuracy by 25.76% and 5.09% on average. By comparing with the accuracy results of existing carbon price prediction models, we discuss the feasibility of improving the prediction effect by increasing the number of similar nodes.

A novel carbon price prediction model based on optimized least square support vector machine combining characteristic-scale decomposition and phase space reconstruction

Carbon trading is an important market mechanism to promote carbon emission reduction and clean development. Accurate carbon price prediction is significant for environmental policymaking and improvement of carbon market efficiency. However, the existence of end effect and chaotic characteristics of carbon price sequence have limited the improvement of carbon price prediction accuracy. In this paper, a novel carbon price prediction model is proposed, which is based on local characteristic-scale decomposition (LCD), phase space reconstruction (PSR) and least square support vector machine (LSSVM) optimized by artificial fish swarm algorithm (AFSA). Firstly, carbon price is decomposed into several intrinsic scale components (ISC) by LCD to capture carbon price characteristics. Secondly, the maximum Lyapunov exponent is used to detect the chaos of the intrinsic scale components, and the chaotic ISC is further reconstructed by phase space reconstruction (PSR). In the meantime, the influence variables of non-chaotic ISCs are selected through partial autocorrelation analysis. Finally, the LSSVM optimized by AFSA is established to predict the ISC components of carbon price series and the ISC components are combined into carbon price prediction results. The empirical analysis shows that LCD-PSR-AFSA-LSSVM model has better prediction accuracy than Comparison models, and the MAPE values of the three carbon markets are 1.23%, 1.49% and 3.27%, respectively. The results suggest that the LCD-PSR-AFSA-LSSVM model is validity, generalization and stability. The application of the model will improve the operation efficiency of carbon market trading and advance clean development of various industries.

A novel hybrid learning paradigm with feature extraction for carbon price prediction based on Bi-directional long short-term memory network optimized by an improved sparrow search algorithm.

An efficient carbon trading market can effectively curb excessive carbon emissions and thus slow down the pace of global warming, which heightens the necessity of improving the accuracy of carbon price forecasting. In order to overcome the weakness of previous prediction model that always trained data in one-way neural networks and propagated the data sequentially, this paper proposes a novel hybrid learning paradigm WPD-ISSA-BiLSTM combining wavelet packet decomposition (WPD), improved sparrow search algorithm (ISSA), and Bi-directional long short-term memory network for deep feature exploration of carbon prices. Firstly, WPD decomposes and reconstructs the original carbon price series into several independent subseries. Then, the input features of the all subseries are filtered with random forest to select the best input features for the prediction model. Finally, a Bi-directional long short-term memorynetwork optimized by the ISSA is employed to deeply delineate the intrinsic evolutionary trends of carbon prices, and the prediction results of all subseries are superimposed on each other to obtain the final carbon price prediction results. The actual carbon emission trading prices are collected as input to the model, and the experimental results show that the RMSE values of the proposed model are 0.2516 and 0.2962 under the mild and severe volatility scenarios, respectively. The proposed model has superiority and robustness compared to the comparison model and several existing models and better understands the intrinsic correlation between historical carbon price data. The results of this study can provide meaningful references for the carbon market development and emission reduction pathways.

A novel interval decomposition ensemble model for interval carbon price forecasting

Accurate carbon price forecasting is of great significance for policy-makers and market participants. However, previous studies only focus on point-valued forecasting and ignore the importance of interval carbon price forecasting. In fact, interval-valued forecasting contains more information and can measure the uncertainty and variability of carbon price. Thus, to predict interval carbon price accurately, we propose a novel interval decomposition ensemble model based on multivariate variational mode decomposition (MVMD) and interval multilayer perceptron (iMLP) optimized by Jaya algorithm. Firstly, MVMD is used to decompose the original interval carbon price series into several sub-series. Secondly, iMLP optimized by Jaya algorithm is constructed to predict each sub-series of the above step. Finally, forecasting results of each sub-series are aggerated into the ultimate predictions of interval carbon price by linear addition. The interval carbon price data from two carbon markets in China are utilized to validate the effectiveness of the proposed model. Experimental results reveal that the proposed model outperforms all the benchmark models and the average values of the interval U of Theil statistics (UI) and the interval average relative variance (ARVI) in two datasets are 0.3003 and 0.0569, respectively. Overall, the proposed model can be used as an effective tool for future interval carbon price forecasting.

Carbon price prediction for China's ETS pilots using variational mode decomposition and optimized extreme learning machine.

With the national goal of “carbon peak by 2030 and carbon neutral by 2060 in China”, studies on carbon prices of China’s Emissions Trading System (ETS) pilots have shown growing interest in the related fields. Carbon price fluctuations reflect the scarcity of carbon resources, and accurate prediction can improve carbon asset management capabilities. Therefore, in order to clarify the dynamics of carbon markets and assign carbon emissions allocation rationally, we propose a hybrid feature-driven forecasting model with the framework of decomposition-reconstruction-prediction-ensemble. In this paper, the non-stationary, nonlinear and chaotic characteristics of carbon prices in China’s ETS pilots have been verified, and then the prediction model is built based on the tested features. Firstly, the original carbon price series are decomposed by Variational Mode Decomposition (VMD), and then reconstructed by Sample Entropy (SE). Next, Extreme Learning Machine (ELM) optimized by Particle Swarm Optimization (PSO) is conducted to predict the subsequences. Lastly, the forecasting series of every subseries are summed to obtain the final results. The empirical results based on carbon prices of China’s ETS pilots proved that the proposed model performs more efficiently than the current benchmark models. As carbon prices are expected to increase across all ETS during the post-COVID-19 recovery stage, the new prediction model will be useful for improving the guiding principles of the existing government policies including the likely introductions of Border Carbon Adjustment (BCA) in the EU and the US, and governing the large global public companies to deliver their “net zero” commitments.