A Sustainable Model for Forecasting Carbon Emission Trading Prices

Abstract

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.

1. Introduction

The “2024–2025 Energy Conservation and Carbon Reduction Action Plan” delineates the concluding phase of energy conservation and carbon reduction within the 14th Five-Year Plan [1,2]. Notable components include the expansion of the national carbon market and the enhancement of the carbon emission quota allocation mechanism [3,4]. As a foundational element of the carbon market mechanism, the carbon price exerts a substantial influence on the efficacy of the plan in reducing CO₂. Fluctuations in carbon prices have a direct impact on the decision-making processes of both enterprises and governments. It is therefore imperative to develop a predictive tool for accurately estimating carbon prices, which is crucial for cost estimation in carbon-consuming industries. Furthermore, it offers indispensable guidance for policymakers and facilitates the formulation of well-informed carbon trading strategies among market participants, with the objective of reducing emission costs [5,6,7].

In recent years, the field of carbon price forecasting has received considerable attention, leading to the development of numerous forecasting models [8]. The current research methods can be classified into two main categories. The first category involves integrating moving average autoregressive models for research purposes. The second category employs econometric models, including generalized autoregressive conditional heteroscedasticity models and value-at-risk models [9,10,11]. This model is founded upon economic theory and employs a synthesis of mathematical and statistical methodologies to discern latent information from data. In a related study, Jingye [12] and colleagues employed the ARIMA model to enhance the precision of their forecasts for the future price trajectory of the EU carbon financial market. Despite the efficacy of this model, the model assumptions are incompatible with the inherent instability and nonlinearity of the time series, resulting in significant discrepancies between the model results and the actual data.

An alternative approach is to employ machine learning algorithms for the analysis of carbon price series data. In comparison to the initial methodology, machine learning models demonstrate superior predictive capabilities [13]. Wang [14] employed random forest (RF) to analyze data from the Chinese carbon trading market, while Sun and Huang [15] utilized backpropagation (BP) neural networks to predict data from the Chinese Hubei Province carbon trading market. Both approaches yielded favorable outcomes. However, the absence of data processing in these studies leaves a significant discrepancy between the predicted and actual results. To enhance the precision of the results, Wei [16] employed a novel dimension reduction technique, s-PCA, to curtail the dimensionality of the variables influencing the Hubei carbon price series. Subsequently, he utilized conventional regression methods and LSTM methods to forecast the carbon price. The experimental results demonstrate that the model exhibits superior accuracy compared to other competing models. However, the research is limited in that it focuses exclusively on traditional carbon price series, and thus fails to consider the impact of other data sets on carbon price series prediction. Mu [17] employed a model integrating swarm intelligence and deep learning algorithms to forecast multi-source data sets incorporating emotional values, thereby enhancing prediction accuracy. With regard to data set processing optimization, Zhu [18] employed empirical mode decomposition (EMD) for the first time to decompose China’s carbon trading market data. In subsequent research, scholars employed variational mode decomposition [19] to decompose the original data set and utilize it as an input parameter for the machine learning algorithm model. The findings of related research indicate that the decomposition algorithm is more effective in processing the original data, thereby enhancing the predictive performance of the model. Nevertheless, these models are not without shortcomings, including mode aliasing, lengthy calculation times, and significant reconstruction errors when decomposing data. There are also studies that combine econometric models, such as GARCH and LSTM neural network hybrid models, to predict carbon prices [20,21].

Additionally, recent studies have explored the dynamic nonlinear linkages between carbon markets, green bonds, clean energy, and electricity markets. By constructing DCC-GARCH and TVP-VAR-SV models, researchers have placed these four markets under a unified framework to analyze volatility risk from a time-varying perspective [22]. Another study found that in highly industrialized countries, the interaction of energy consumption and industrialization significantly increases carbon emissions, suggesting the need for policies promoting green energy for industrial activities [23].

As previously stated in the review, while scholars have made notable advancements in the field of carbon price prediction, there are still significant shortcomings. For instance, there is a dearth of an efficacious prediction apparatus. The decomposed data exhibit modal aliasing, the model operation time is protracted, the flexibility is insufficient, the dataset is limited in scope, and the prediction accuracy is inadequate.

This paper makes the following primary contributions to the field:

(1)

The ICEEMDAN-MSE decomposition-reconstruction algorithm is utilized to decompose the original data set into intrinsic mode functions (IMFs), thereby effectively resolving the modal aliasing issue associated with IMF components.

(2)

Subsequently, the multi-scale entropy of each IMF component is calculated, and the input sequence of the neural network model is reconstructed using multi-scale entropy, thereby markedly reducing the complexity of the prediction.

(3)

An intelligent optimization algorithm is employed to optimize the hyperparameters of the LSTM network, thereby enabling the network to adaptively seek optimal performance, improve prediction accuracy, and ensure model flexibility.

(4)

This paper presents the first analysis and prediction of carbon emission trading prices for the Chinese and EU carbon markets, thereby effectively verifying the robustness and scientific validity of the model.

2. Methods

This paper focuses on the transaction price of carbon as the core research subject. It employs the fully adaptive noise ensemble empirical mode decomposition (ICEEMDAN) model to decompose the original carbon price data and calculates multi-scale entropy (MSE) for each decomposed sequence. Using the MSE of the original data as a threshold, the decomposed sequences are reconstructed into input sequences. Carbon price series typically exhibit significant nonlinearity and complexity, making traditional linear econometric models inadequate for capturing their dynamic changes. The improved EMD (ICEEMDAN) used in this study effectively addresses issues of module aliasing and excessive noise by adding noise after each decomposition, thereby more accurately capturing the characteristics of the carbon price series. Utilizing MSE to reconstruct the intrinsic mode functions (IMFs) significantly reduces prediction complexity. This study employs the Gray Wolf Optimization (GWO) algorithm to adaptively tune the hyperparameters of the Long Short-Term Memory (LSTM) network, enhancing prediction accuracy while maintaining model flexibility. The input sequences are fed into the improved LSTM network model for prediction, and the results are aggregated to compute the final predicted sequence. For comparative analysis, this study uses ARIMA, GRU, and LSTM models as benchmark models. The model’s accuracy is evaluated using metrics such as RMSE, MAE, MAPE, and Accuracy. Additionally, the model’s robustness is tested by predicting the prices in the world’s largest carbon spot trading market. The prediction framework of this model is illustrated in Figure 1.

2.1. ICEEMDAN Algorithm

ICEEMDAN is a non-linear, non-stationary data processing method based on the EMD and EEMD methods. It has the characteristics of rapid calculation speed and a minimal reconstruction error, as evidenced in the referenced literature. [24]. ICEEMDAN is a method based on CEEMDAN that proposes the addition of the kth intrinsic mode function after EMD decomposition as a means of improving the quality of the resulting noise. The noise improvement simultaneously addresses the issues of mode aliasing and the presence of excessive noise residuals while enhancing the decomposition efficiency of the carbon price series [25]. The following section outlines the implementation process of ICEEMDAN.

Let us suppose that the original signal is x and that I sets of white noise are added to it. The signal sequence at the i time can be expressed by the following equation:

$$d^i(t)=d(t)+{\epsilon }_{0}E(w^{(i)}),i=1,2,\dots I$$

(1)

The question thus arises as to the location of the Gaussian white noise. In this context, the i-th signal sequence is defined as ε, which represents the standard deviation of the noise. The processed signal is then decomposed by EMD, and the components obtained by decomposition are averaged. This process is illustrated in the first modal component.

$$IM{F}_1(t)=I^{-1}{\displaystyle {\sum }_{i=1}^{I}IM{F}_1(t)}$$

(2)

In this context, the term “IMF” refers to the intrinsic mode functions, while “IMF_k” denotes the kth mode component. The initial residual signal (k = 1) is defined as r₁(t) = d(t) − IMF₁(t), and white noise is subsequently introduced to calculate the subsequent residuals. Subsequently, the signal r₁(t) + E₁[wnⁱ(t)] is decomposed further to obtain the second mode component. In the subsequent stage, the kth residual signal and the (k + 1)th mode component can be calculated as follows:

$$r_k(t)=E(w^i)r_{k-1}(t)-IM{F}_k(t)$$

(3)

$$IM{F}_{K+1}(t)=I^{-1}{\displaystyle {\sum }_{i=1}^I{E}_1\{r_k(t)+{\epsilon }_k{E}_k[w{n}^i(t)]\}}$$

(4)

The process should be repeated (3) and (4) until the remaining ingredients no longer meet the requisite decomposition conditions. Ultimately, the original signal, d(t), is decomposed into the following:

$$d(t)={\displaystyle {\sum }_{i=1}^{k}IM{F}_1(t)+R(t)}$$

(5)

where R(t) is the final residual amount.

2.2. Multi-Scale Entropy Theory

The concept of multi-scale entropy (multi-development) is founded upon a methodology for measuring the complexity of time series, which is employed in SPEN to assess the degree of similarity and complexity exhibited by time series at varying scales [26]. This is the first occasion on which the carbon price series has been subjected to coarse processing. Coarse processing refers to the act of downsampling a time series, thereby creating signals at varying scales. In particular, let us consider a time series x = {x₁, x₂, …}. The coarsened time series, y(τ), can be defined as follows [27]:

$$\begin{array}{l}{y}_j^{\tau }={\displaystyle \frac{1}{\tau }}{\displaystyle {\sum }_{i=(j-1)\tau +1}^{j\tau }{x}_i}, 1\le j\le N/\tau \\ \end{array}$$

(6)

where τ represents the time scale.

The sample entropy for each scale should be calculated. The formula for calculating the sample entropy is as follows:

$$SampEn(m,r,y^{(\tau )})=-\ln {\displaystyle \frac{B_m(r)}{A_m(r)}}$$

(7)

where m is the embedding dimension, r is the similarity threshold, and B_m(r) and A_m(r) are the number of template vector matches, respectively. Specifically, for each template vector of length m, we can calculate the distance between it and other template vectors $d[y_i^{\tau },y_j^{\tau }]={\max }_{k=0}^{m-1}\left|y_{i+k}^{\tau }-y_{j+k}^{\tau }\right|$. Then we define the indicator function $I(d[r_i^{\tau },r_j^{\tau }]\le r)$, and count $B_m(r)={\displaystyle \frac{1}{N-m+1}}{\displaystyle {\sum }_{i=1}^{N-m+1}I(d[r_i^{\tau },r_j^{\tau }]\le r)}$ and $A_m(r)={\displaystyle \frac{1}{N-m}}{\displaystyle {\sum }_{i=1}^{N-m}I(d[r_i^{\tau },r_j^{\tau }]\le r)}$. Finally, we can obtain a set of multi-scale entropy values where M$\{SampEn(m,r,y^{(\tau )}),1\le i\le M\}$ is the largest time scale.

2.3. GWO-LSTM Model

The objective of this research is to enhance the prediction capacity of the LSTM network by employing the GWO optimization algorithm. To accomplish this, we optimize two key parameters: the number of hidden neurons in the LSTM network and the number of training iterations for the LSTM model [28]. The flowchart of the GWO-LSTM model is presented in Figure 2 for the reader’s convenience.

The Grey Wolf Optimizer (GWO) is a specific type of swarm optimization algorithm, as outlined in reference [29,30]. The primary process of the GWO algorithm entails the initialization of the grey wolf population, the updating of the positions of the α, β, and δ wolves, the updating of the position of the ω wolf, and the repetition of this sequence multiple times. In each iteration, the grey wolf ω updates its position based on the positions of α, β, and δ, thereby facilitating a more effective search of the solution space. Let us assume that t represents the current iteration, and that is a vector of coefficients that decrease linearly from 2 to 0 at random. Let us also assume that is the position vector of the target and that is the position vector of the grey wolf. In this case, the mathematical expression of the algorithm is as follows:

$$\overrightarrow{D}=\left|\stackrel{\rightharpoonup }{C}.\overrightarrow{X_p(t)}-\overrightarrow{X(\mathrm{t})}\right|$$

(8)

$$\overrightarrow{X}(t+1)=\overrightarrow{X_p(t)}-\overrightarrow{A}.\overrightarrow{D}$$

(9)

LSTM is a variant of recurrent neural networks that is specifically designed to process long sequences of data and learn long-term dependencies [31]. The LSTM network is a specific type of recurrent neural network (RNN) that consists of memory cells, input gates, output gates, and forget gates [32,33]. The implementation steps are as follows:

The output vector obtained by the input vector of the input gate through the activation function is calculated at time t as follows:

$${a_l}^t={\displaystyle {\sum }_{i=1}^l{w}_{il}{x_l}^t+{\displaystyle {\sum }_{h=1}^H{w}_{hl}{b_h}^{t-1}+{\displaystyle {\sum }_{c=1}^C{w}_{cl}{b}_c^{t-1}}}}$$

(10)

$$b_l^t=f(a_l^t)$$

(11)

The input vector of the input layer neuron at time t represents the input vector of the input layer neuron at time t, the output vector of the previous hidden layer, the information retained by the memory unit at the previous time, and the weight matrix of the input information and each neuron. Similarly, the input to the forget gate is composed of three parts, analogous to that of the input gate. The output vector at time t is calculated according to the following formula:

$${a_{\delta }}^t={\displaystyle {\sum }_{i=1}^l{w}_{i\delta }{x_i}^t+{\displaystyle {\sum }_{h=1}^H{w}_{h\delta }{b_h}^{t-1}+{\displaystyle {\sum }_{c=1}^C{w}_{c\delta }{b}_c^{t-1}}}}$$

(12)

$$b_{\delta }^t=f(a_{\delta }^t)$$

(13)

The input to the memory cell consists of two parts, including the input vector and the output of the previous hidden layer. The formula for calculating the memory cell at time t is:

$${a_c}^t={\displaystyle {\sum }_{i=1}^l{w}_{ic}{x_i}^t+{\displaystyle {\sum }_{h=1}^H{w}_{hc}{b_h}^{t-1}}}$$

(14)

The memory unit decides whether to retain past information based on the judgment of the forgetting gate. The calculation formula is as follows:

$${s_c}^t=b_{\delta }^t{s}_c^{t-1}+b_l^{t}g(a_c^t)$$

(15)

where g is the result of the activation function memory unit, the input is entered into the activation function to obtain the final result. The calculation formula is as follows:

$$b_h^t=oh(s_c^t)$$

(16)

Once the final result has been obtained, the LSTM backpropagation process minimizes the loss function and adjusts the weight parameters [34]. This eliminates the gradient explosion problem and improves the prediction accuracy of the model. The GWO optimization algorithm is employed to identify the optimal number of hidden layers and the number of iterations for the LSTM model, thereby markedly enhancing the learning efficiency of the LSTM model.

3. Experimental Verification

This experiment is centered on the carbon price sequence, and experiments are presented that are designed to compare models and to test the impact of removing specific elements from models. The benchmark models utilized in the model comparison experiments primarily encompass the following: The models employed in this study include the ARIMA, BP neural network, GRU network model, and LSTM network model. The ablation experiment mainly conducts a longitudinal comparison of this model system to verify the integrity and scientific validity of the model system.

3.1. Data Source

The data presented in this article were sourced from the CO₂ Trading Network (http://www.tanpaifang.com/), accessed on 18 September 2023. Figure 3 illustrates that the Chinese carbon market exhibited consistent growth from 2013 to 2017, with a stabilization of trading volume between 30 and 50 million tons observed in 2018 and subsequent years. Notably, the carbon exchanges in Hubei, Guangdong, and Shenzhen represent a significant portion of the national market, exhibiting high data integrity and substantial research value. The data set pertaining to EU CO₂ trading prices is derived from the wind database, and it is more comprehensive than the corresponding data set for the Chinese carbon exchange.

Table 1. Data span schedule.

	Guangdong	Chongqing	Shenzhen	Beijing	Tianjin	Shanghai	Fujian	EU
2014/04/02–2023/01/13	2013/12/19– 2023/01/13	2014/06/19–2022/12/11	2013/08/15–2023/01/12	2013/11/28–2023/01/05	2013/12/26–2023/01/13	2013/12/29–2023/01/13	2017/01/09–2021/01/13	2005/04/22–2021/09/06

illustrates the temporal scope of CO₂ trading across the various exchanges.

3.2. Data Preprocessing

In our study, we performed sequential resampling to maintain the temporal dependencies inherent in the time series data. This approach ensures that the order of data points is preserved, which is crucial for accurate modeling and prediction.

(1)

Data Decomposition and Reconstruction

This paper utilizes the ICEEMDAN model to decompose the original data set, thereby generating an unknown number of flat data sets, or modal components. As illustrated in Figure 4, the resulting decomposition is presented. As illustrated in the figure, the carbon price data, following noise reduction by the ICEEMDAN model, exhibits a notable degree of smoothness and exhibits reduced fluctuations in comparison to the original carbon price data. This approach effectively reduces errors. As an illustration, the carbon price series in Hubei and Shenzhen exhibit considerable volatility in Figure 4a,d, whereas the carbon price series in Fujian displays less fluctuation in Figure 4h. In contrast, the carbon price series in the European Union demonstrates stability in Figure 4i, indicating that the price of EU emission allowances is relatively constant. Each carbon price series is divided into multiple intrinsic mode functions (IMFs) and trend components. In each series, the trend component represents the final IMF component.

Following the ICEEMDAN decomposition, the multi-scale entropy of the sub-sequence is calculated, and the sub-sequence is reconstructed into three data sets in accordance with the multi-scale entropy of the initial sequence, which is used as the threshold. The sub-sequence that falls below the specified threshold is classified as a low-frequency sequence, while the sub-sequence above the threshold is designated as a high-frequency sequence. Ultimately, the IMF component represents the trend sequence.

Table 2. Multi-scale entropy statistics of carbon price series.

Carbon Market	Initial Sequence	IMF1	IMF2	IMF3	IMF4	IMF5	IMF6	IMF7	IMF8	IMF9	IMF10	IMF11
Shenzhen	0.87	0.98	0.73	0.58	0.57	0.37	0.21	0.02	0.05	0.02	0.97	-
GuangDong	0.11	0.43	0.31	0.34	0.28	0.25	0.09	0.02	0.02	0.00	0.76	-
Tianjin	0.17	0.26	0.31	0.32	0.29	0.21	0.10	0.06	0.01	0.00	0.66	-
Hubei	0.22	0.93	0.71	0.58	0.40	0.15	0.05	0.01	0.00	0.86	-	-
Beijing	0.31	0.48	0.40	0.38	0.36	0.19	0.09	0.06	0.00	0.84	-	-
Shanghai	0.34	0.853	0.6	0.57	0.49	0.11	0.04	0.01	0.56	-	-	-
Fujian	0.68	1.44	0.60	0.59	0.51	0.32	0.04	0.01	0.75	-	-	-
Chongqing	0.30	0.81	0.58	0.37	0.40	0.14	0.05	0.01	0.90	-	-	-
EU	0.05	0.62	0.30	0.34	0.22	0.13	0.06	0.01	0.01	0.01	0.01	0.83

(Note: the black mark is the multiscale entropy value of the initial sequence,—means that this sequence has no such component).

illustrates the multi-scale entropy of the carbon price sequence. To illustrate, in the Hubei carbon price market, the first four IMFs are high-frequency sequences, the next four are low-frequency sequences, and the final IMF is a trend sequence. The data in each sequence are accumulated to form three distinct sequence sets: a high-frequency sequence set, a low-frequency sequence set, and a trend sequence set.

(2)

Data normalization

It is not uncommon for assessment indicators to vary in dimensions and units of measurement. To circumvent the impact of these dimensional disparities, data normalization techniques are applied. This process involves transforming the reconstructed dataset of carbon prices to fall within predefined ranges, thereby standardizing the data for consistent analysis. In addition, the detrimental effects of single-sample data can be mitigated [35]. The data normalization equation is.

$$z_n={\displaystyle \frac{z_i-z_{\min }}{z_{\max }-z_{\min }}}$$

(17)

where n denotes the sample size; $z_n$ is the normalized data; $z_i$ is the original data; $z_{\max }$ and $z_{\min }$ denote the minimum and maximum values of the carbon price transaction sequence data, respectively. The predictive outcomes for each dataset are aggregated through the application of the GWO-LSTM technique. Subsequently, the datasets are subjected to a denormalization process in accordance with Equation (18), thereby restoring them to their original value range.

$$f_i=f_n(z_{\max }-z_{\min })+z_{\min }$$

(18)

(3)

Data set division

In this study, the normalized carbon price sequence is divided into segments of equal length, with 90% of the data utilized for training and 10% for testing. The training set is employed to train the model and identify suitable model parameters, while the test set is utilized to assess the model’s operational accuracy and efficiency. In the present study, the length of the sliding window is set to seven. The initial seven historical data points are employed to forecast the carbon trading price on the first day following the subsequent week.

3.3. Evaluation Indicators

The prediction errors in the analyzed test set were evaluated using four indicators: MAE, RMSE, MAPE, and Accuracy. These indicators were used to assess the prediction errors of the model. In general, the lower the first three indicators, the lower the model error. Additionally, the closer the latter indicator is to 1, the better the fit of the model. The specific calculation formula is as follows:

$$MAE={\displaystyle \frac{1}{n}}{\displaystyle {\sum }_{t=1}^n\left|A_t-F_t\right|}$$

(19)

$$RMSE=\sqrt{{\displaystyle \frac{1}{n}}{\displaystyle {\sum }_{t=1}^n\left|A_t-F_t\right|}}$$

(20)

$$MAPE={\displaystyle \frac{100\%}{\mathrm{n}}}{\displaystyle {\sum }_{t=1}^n\left|\frac{A_t-F_t}{A_t}\right|}$$

(21)

$$Accuracy=1-{\displaystyle \frac{100\%}{n}}{\displaystyle {\sum }_{t=1}^n\left|\frac{A_t-F_t}{A_t}\right|}$$

(22)

where $A_t$ can represent the actual value of t at that time $t_t$; $F_t$ is the predicted value at time t.

3.4. Experimental Parameter Settings

The benchmark models for this experiment are the Autoregressive Integrated Moving Average (ARIMA), the Gated Recurrent Unit (GRU), and LSTM models. The ARIMA model parameters are configured to permit the flexible setting of the AR autocorrelation coefficient and MA autocorrelation coefficient in accordance with the AIC value. The BP neural network model parameters are set to two hidden layers, a learning rate of 0.001, 100 iterations, a data input length of 7, and an output of 1. The GRU model parameters are set to two hidden layers, 256 neurons per layer, 100 training iterations, and the LSTM model parameters are set to the same specifications as the GRU model. The optimizer employs the Adam algorithm. The GWO algorithm in this model is configured to optimize the number of variables to two, the minimum value limit to one, the number of grey wolves to fifty, and the maximum number of iterations to two.

4. Results

The model employs the GWO optimization algorithm to enhance the hyperparameters of the LSTM model, facilitate autonomous learning of the optimal number of network layers, and determine the optimal number of iterations. The model demonstrates a notable enhancement in efficiency and calculation speed. As illustrated in Figure 5, the model’s predictive data exhibits a high degree of concordance with the actual data. As illustrated in Figure 5a, the model is capable of discerning the peaks and troughs of the actual values, thereby achieving the most optimal overall fitting effect. However, due to the lack of integrity of the carbon price series, the model is more sensitive to the peaks in Figure 5b, resulting in greater fluctuations.

Table 3. Model error table.

Carbon Market	Error Indicator	ARIMA	BP	GRU	LSTM	ICEEMDAN-MSE-GWO-LSTM
EU	MAE	10.68	16.97	16.41	4.18	0.04
	RMSE	15.15	20.83	18.77	6.69	0.22
	MAPE (%)	42.09	40.76	34.00	11.29	0.5
	Accuracy (%)	57.90	59.24	66.00	88.71	99.48
Hubei	MAE	1.44	12.67	3.97	2.25	0.44
	RMSE	1.85	12.76	5.33	2.43	0.66
	MAPE (%)	2.90	36.42	9.84	4.98	0.9
	Accuracy (%)	97.01	63.58	90.15	95.02	99.06
hillsides	MAE	8.94	20.78	8.40	7.13	2.66
	RMSE	10.89	21.30	13.83	8.68	1.63
	MAPE (%)	13.37	37.23	15.07	10.02	3.40
	Accuracy (%)	86.63	62.77	84.29	89.82	96.60
Chongqing	MAE	4.52	9.47	8.75	5.26	0.76
	RMSE	5.47	10.17	6.98	7.78	0.87
	MAPE (%)	13.11	33.31	22.99	7.69	1.99
	Accuracy (%)	86.89	66.69	77.00	92.52	98.01
Shenzhen	MAE	14.74	3.80	29.09	3.51	1.65
	RMSE	15.16	5.33	33.26	2.55	1.28
	MAPE (%)	37.65	46.85	57.55	19.87	3.35
	Accuracy (%)	62.34	53.15	42.45	80.13	96.65%
Beijing	MAE	34.74	23.54	50.43	15.52	11.74
	RMSE	40.31	28.29	56.47	21.16	3.42
	MAPE (%)	54.72	31.01	34.75	25.19	13.87
	Accuracy (%)	45.28	68.99	65.25	74.81	86.13
Tianjin	MAE	8.43	2.75	6.93	3.62	0.60
	RMSE	9.84	3.76	7.91	4.24	0.77
	MAPE (%)	39.36	9.51	20.41	12.16	2.01
	Accuracy (%)	60.64	90.49	79.58	87.84	97.99
Shanghai	MAE	5.03	16.26	3.52	4.59	0.56
	RMSE	5.77	16.39	4.38	5.14	0.75
	MAPE (%)	8.02	39.45	6.48	7.78	1.01
	Accuracy (%)	91.97	60.55	93.52	92.22	98.99
Fujian	MAE	3.27	3.37	3.21	1.38	1.07
	RMSE	4.06	4.24	3.99	1.59	1.03
	MAPE (%)	19.77	18.02	18.99	9.59	7.41
	Accuracy (%)	80.23	81.98	81.01	90.41	92.59

presents the error results, which are expressed in terms of mean absolute error (MAE), root mean square error (RMSE), mean absolute percentage error (MAPE), and accuracy. These metrics are utilized to assess the discrepancy between the actual and predicted values, as well as the quality of the model. In comparison to the basic model, the MAPE and accuracy have been enhanced, indicating that the stability and flexibility of the model have been markedly improved, and the overall average prediction accuracy has increased to 95.75%. In carbon price markets with stronger data integrity, such as those in Hubei, Guangdong, Shenzhen, and the European Union, the prediction accuracy of the model is significantly higher than that of other models. For instance, in the Hubei carbon price market, the accuracy of the ARIMA model is 2.05% higher than that of the ARIMA model, 8.91% higher than that of the GRU model, and 4.04% higher than that of the LSTM model. The MAE and RMSE have increased to 0.44 and 0.66, respectively, which is significantly higher than that of the benchmark model. In carbon price markets with low trading volumes, such as the Fujian carbon price market, the prediction accuracy of this model is, on average, 8.71% higher than that of the benchmark model. The mean absolute error (MAE) increased by 1.55, and the root mean square error (RMSE) increased by 2.18, indicating a significant improvement overall.

Melting Experiment

In this study, we selected the carbon trading market with the most complete data and high model accuracy as the research object of the ablation experiment. We then compared the prediction performance of the CEEMDAN-LSTM, CEEMDAN-MSCE-LSTM, and CEEMDAN-MSCE-GWO-LSTM models in the Hubei and EU carbon price markets. The results of the experiment are presented in

Table 4. Comparison of ablation experiments.

Carbon Market	Error Indicator	CEEMDAN-LSTM	CEEMDAN-MSCE-LSTM	CEEMDAN-MSCE-GWO-LSTM
Hubei	MAE	1.73	1.04	0.42
	RMSE	1.31	1.43	0.65
	MAPE (%)	3.79	1.81	0.09
	Accuracy (%)	96.21	98.19	99.10
EU	MAE	1.68	1.97	0.41
	RMSE	1.15	0.83	0.77
	MAPE (%)	2.09	2.76	0.40
	Accuracy (%)	97.91	97.24	99.60

.

As evidenced in Table 4, the CEEMDAN-MSCE-GWO-LSTM model demonstrates notable superiority in all error indicators. In the Hubei market, the mean absolute error (MAE), root mean square error (RMSE), and mean absolute percentage error (MAPE) of this model are 0.42%, 0.65%, and 0.09%, respectively. In the EU market, these values are 0.41%, 0.77%, and 0.40%, respectively. Moreover, the model demonstrated a high degree of accuracy in forecasting, with success rates of 99.10% and 99.60% in the two markets, which were significantly higher than those of the other two models. While the CEEMDAN-MSCE-GWO-LSTM model demonstrated satisfactory accuracy, there is potential for enhancement in its operational efficiency. Further research could be conducted to enhance the computational efficiency of this model, thereby achieving a more optimal balance between accuracy and efficiency in practical applications.

5. Conclusions

In conclusion, this paper puts forth a novel carbon trading prediction system, comprising the following principal contributions:

(1) Superiority of the model: The ICEEMDAN-MSCE-GWO-LSTM model proposed in this paper demonstrates superior performance in predicting carbon trading prices, with an accuracy rate that is approximately 3.1% and 0.91% higher than that of the traditional ICEEMDAN-LSTM and ICEEMDAN-MSCE-LSTM models, respectively.

(2) Applicability to Multiple Markets: The experimental results demonstrate that the model exhibits robust performance not only on the EU carbon price series but also on the carbon price series of the seven major carbon trading markets in China, thereby substantiating its broad applicability.

The ability to predict carbon prices can assist in reducing the costs associated with carbon emissions for industries that consume significant amounts of carbon, including manufacturing, power, and heat industries. Furthermore, it can encourage these enterprises to develop low-carbon technologies, thereby reducing carbon emissions. This paper presents a predictive analysis of data from the world’s largest carbon spot trading market, highlighting the policy significance of accurate carbon price predictions in supporting cost-effective carbon reduction strategies and promoting sustainable practices. CO₂ [36,37,38].

Considering the aforementioned conclusions and the limitations of this study, the following avenues for future research are proposed:

(1) Model efficiency factors. While the ICEEMDANMSCE-GWO-LSTM model demonstrates satisfactory accuracy, there is potential for enhancement in its operational efficiency. Further research could yield improvements in the computational efficiency of the model, thereby achieving a more optimal balance between accuracy and efficiency in practical applications.

(2) Market activity factors. Different carbon trading markets have different levels of activity. According to relevant research, Hubei’s carbon trading market is relatively stable with a low return on investment, while Shanghai’s carbon trading market is more influential and customers need to bear more risks [39].

(3) Accounting factors pertaining to carbon sinks. The objective of carbon sink accounting is to ascertain the reduction in emissions resulting from carbon emission rights trading and to reflect this in the carbon price. In the event of inaccurate carbon sink accounting results, there is a possibility that the cost of emission reduction may be underestimated, which could have an adverse impact on the carbon price [40]. The system proposed in this paper does not take into account the potential impact of inaccurate carbon sink accounting on carbon price trading. In the event of inaccurate carbon sink accounting results, there is a possibility of an underestimation of the emission reduction amount, which may subsequently lead to a reduction in the willingness to reduce emissions and, consequently, affect the carbon price. It would be beneficial for future research to include the accuracy of carbon accounting as a potential variable in the system.