Research on Influencing Factors of Carbon Market Price and Machine Learning Pricing Prediction: Empirical Analysis Based on Seven Carbon Markets in China

Abstract:carbon trading market is an important tool to cope with climate change and realize low-carbon economy transition. The price formation mechanism and influencing factors of carbon trading market have attracted increasing attention. However, most of the existing studies focus on theoretical discussions, lacking empirical analysis of the seven carbon trading markets in China. This paper uses differential econometric models and machine learning algorithms (including decision trees, random forests and Xgboost) to analyze carbon trading market data from 2014 to 2023 to explore the impact of macroeconomic factors on carbon trading prices. The results show that there is a significant negative correlation between macroeconomic factors and carbon trading price, and machine learning model is better than traditional linear regression model in predicting carbon trading price. The research of this paper provides an important reference for improving the efficiency of carbon trading market and formulating relevant policies.

Keywords:carbon trading; econometric differential model; machine learning

I. Introduction

The theoretical focus of carbon trading market is "Pigou tax" and "Coase law", the logic of internalizing carbon emission externality cost in carbon trading market mainly lies in total amount control and trading system design, and the hidden economic principle behind carbon trading is "green premium"(Sun Xia et al., 2024)^[3]. Behind this system design reflects the simple concept of justice of "who pollutes, who governs; who develops, who protects". As an important tool to cope with climate change and realize low-carbon economy transition, carbon trading market has attracted more and more attention in recent years. With the global emphasis on carbon emission control, countries have established and improved carbon trading markets to promote efficient allocation of resources and technological innovation. China, as the world's largest carbon dioxide emitter, is of great significance to promote the transformation of low-carbon economy for achieving sustainable development. The primary goal of low-carbon economy transition is to reduce carbon emissions, and the impact of traditional energy consumption structure makes carbon emissions from energy consumption the most important source of emissions at present.

Existing research shows that efficient carbon markets can effectively reflect the true cost of carbon emissions and thus guide companies to adopt low-carbon technologies. Although carbon trading market has many advantages, there are still many limitations in practice, such as limited market development, low trading frequency and low offset ratio of certified emission reductions. These problems may be related to insufficient incentives and limited coverage of carbon trading markets. Therefore, it is of great theoretical and practical significance to deeply analyze the factors affecting carbon trading price, especially the role of macroeconomic factors.

The innovation of this paper lies in using machine learning method to deeply analyze the pricing problem of carbon trading market, overcoming the limitation of traditional forecasting model affected by data frequency and other factors, so as to improve the accuracy of forecasting results. Although the existing literature affirms the positive role of carbon trading in energy conservation and emission reduction, the imperfections of the market lead to its inefficiency, unfair competition and manipulation. Therefore, this paper will select the data of China's seven carbon trading markets from 2014 to 2023 to analyze the impact of macroeconomic factors on carbon trading prices, aiming to improve the efficiency of carbon trading markets and provide reference for the formulation of relevant policies. The structure of this paper is as follows: the second part is literature review, the third part introduces research design and methods, the fourth part presents empirical results, and the fifth part is conclusions and recommendations.

II. Literature review

Carbon trading market is an important tool to cope with climate change and realize low-carbon economic transformation. With the emphasis on carbon emission control, how to improve the efficiency of carbon trading market, optimize resource allocation and promote technological innovation has become the focus of academia and policy makers. This paper reviews the related literatures and discusses the importance of improving the efficiency of carbon trading market, the factors affecting carbon trading price, the limitations of the market and the corresponding solutions.

An efficient carbon market can effectively reflect the true cost of carbon emissions, thus guiding enterprises to adopt low-carbon technologies and achieve efficient allocation of resources. Xu Jianwei and Liu Zhihua (2024) pointed out that China, as a major CO2 emitter, promoting the transformation of low-carbon economy is of great significance for implementing the concept of green and low-carbon development. The primary goal of low-carbon economic transformation is to reduce carbon emissions, and due to the influence of traditional energy consumption structure, carbon emissions generated by energy consumption are the most important source of emissions at present and also the focus of carbon emission reduction in the future^[5]. At the same time, Wu Zhenni et al.(2024) emphasized that, from the perspective of implied carbon emissions, the implementation difference of carbon trading policy will increase the uneven distribution of carbon emission reduction responsibilities between pilot areas and non-pilot areas, enriching the relevant conclusions of the current research on the impact of carbon trading pilot policy on implied carbon emissions between regions^[4]. Although carbon trading markets have many advantages, there are still many limitations in practice. Luo Liangwen et al.(2024) pointed out that the domestic carbon emission trading market still faces some challenges, such as limited market development, inability to be applied on a large scale, low trading frequency, low offset ratio of certified emission reductions, complex offset procedures, and difficulty in mobilizing market enthusiasm. This may be related to insufficient incentives in the carbon trading market, or it may be due to the limited coverage of carbon trading, resulting in poor implementation of policies^[2]. Sun Xia and Liang Hongzhi (2024) emphasize that the phenomenon of hidden carbon emission transfer not only affects the emission reduction effect, but also may lead to unfair competition among regions. In addition, the market mechanism is not perfect, and the lack of regulatory measures makes the market vulnerable to manipulation, similar to Zhao et al. (2023)^[7].

Carbon trading price is the result of many factors. Accordingto Gao Kaiet al.(2024), policy regulation, market supply-demand relationship and various external economic environments will affect the fluctuation of carbon trading price^[1]. Specifically, policy uncertainty tends to lead to market participants 'expected volatility of future prices, exacerbating market instability. (2019) points outthat transparency and information symmetry of markets also play an important role in price formation, and that information asymmetry may lead to manipulation by some participants^[12]. In addition, Fang et al. (2023) Further research shows that there is a significant interaction between technological innovation breakthroughs and carbon trading policies, and a good policy environment can promote technological progress and thus affect carbon trading prices^[89]. A deep understanding of the dynamics and complexity of carbon markets is therefore fundamental to effective policy formulation.

To sum up, the existing literature affirms the positive role of carbon trading in energy conservation and emission reduction, but at the same time, due to the imperfections of the market, there are problems such as inefficiency, unfair competition and even manipulation. Therefore, this paper selects the data of seven carbon trading markets in China from 2014 to 2023 to analyze the impact of macro indicators on carbon trading, which can not only improve the efficiency of carbon trading market, but also provide direction for formulating relevant policies.

III. Study design

(i) Research methods

1. differential econometric model

In this chapter, to simplify the research process and establish effective econometric models, we will construct linear models for the relationship between financial asset returns and macroeconomic factors in each pilot market. Specifically, we use the Differenced Econometric Model, which improves the robustness and predictive power of the model by differentiating the time series data to eliminate non-stationarity and seasonal fluctuations.

represents the difference in logarithm of valence,Lrepresents the lag factor, andXrepresents the vector of explanatory variables. When constructing the linear model, the variables selected mainly include the trading prices of the seven major trading markets, the indexes of the domestic stock market, the major energy sources and the US stock index.

The basic idea of differential econometric models is to eliminate trend components and periodic fluctuations in the data by calculating the differential value of the variable (i.e., the difference between the current value and the previous value), so that the data are more consistent with the stationarity assumption. This process not only helps to improve the explanatory power of the model, but also effectively reduces the influence of autocorrelation on the regression results. After differential processing, the model can more accurately capture the dynamic relationship between carbon trading prices and macroeconomic factors.

2. decision-making tree

Zhou Liang (2022) defines three machine learning models in turn as basic modeling^[6]. Threemachine learning algorithms based on decision treeare CART decision tree algorithm, Bagging ensemble algorithm based random forest algorithm and Boosting ensemble algorithm based Xgboost algorithm. CART decision trees select attributes by comparing the Gini index of each attribute.

where $$ is the sum of t decision trees for the sample as the predicted value, f is the tth regression tree, and F is the set space of all regression trees.

3. random forest

Random Forest (RF) is an ensemble learning method that uses voting to combine prediction results, assigning the category with the most votes as the final output. Random forest can handle very large amounts of data, and its error rate for most learning tasks is almost at the same level as any other method, with a smaller tendency to overfit.

Building a loss function based on the decision tree:

where lrepresentsthe deviation between thepredicted value $$ and the true value , Ω represents the complexity of each tree, and the calculation formula is:

where T is the number of leaf nodes, w is the weight of leaf nodes, γ and λ are regular coefficients.

4. gradient hoist

Xgboost is proposed on the basis of the traditional GBDT model and is a new gradient-lifting ensemble learning method. Compared with GBDT, Xgboost uses second-order Taylor expansion to increase regularization term to seek optimal solution of loss function, avoiding overfitting to some extent.

Based on the first two formulas,Xgboost Taylor expands the loss functionto quadratic terms at $$ , and transforms the optimization objective into a problem of solving the minimum of a quadratic function in one variable under the given decision tree structure. Then we try to segment the leaf nodes by greedy algorithm and compare the gain of objective function before and after segmentation until we get the optimal model.

5. performance evaluation

In order to evaluate the predictive performance of the above four models,mean absolute error (MAE) and root mean square error (RMSE) areusedas evaluation indicators of model goodness of fit^[6], which are calculated as follows:

N represents the sample size, $$ and represent the predicted and observed values of the sample, respectively. The smaller the MAE and RMSE, the better the model fit.

(ii) Variable settings

The data in this article comes from Wind database, using monthly data from 2014 to 2023 to comprehensively show the changing trend of carbon trading market. Referring to Zeng et al.(2023), this study sets the average transaction price of carbon trading (yuan/ton) as the explained variable^[137], and divides the explanatory variables into the following categories:

1. Stock index category: including Shanghai index, Shenzhen index, energy index, raw material index, industrial index, bond yield;

2. Energy price category: covering raw coal price (yuan/ton), steel price (yuan/ton), ore price (yuan/ton), liquefied natural gas price (yuan/ton), gasoline price (yuan/ton) and crude oil price (yuan/ton), among which raw coal price selects Dongsheng price in Inner Mongolia, gasoline price selects No.95 gasoline price^[11];

3. U.S. stock index category: including Nasdaq index and Dow Jones index.

(iii) Descriptive statistics

Table1Sample observation time and data

This paper collects trading activity in China's seven major carbon trading markets from January 1, 2014 to December 31, 2023, reflecting significant differences in non-zero trading days and their proportions. The non-zero trading days in Shenzhen market are 2027 days, accounting for 55.50% of the total observation days, showing high trading activity; while the non-zero trading days in Tianjin and Chongqing markets are only 897 days and 843 days respectively, with the proportion as low as 24.56% and 23.08%, indicating that their trading activity is relatively low. These differences may be closely related to factors such as market mechanism, policy environment and participant base, especially the proportion of non-zero trading days in Guangdong and Hubei markets is 58.65% and 61.28% respectively, further emphasizing the diversity of market activity.

Table2Descriptive statistical results of data indicators

The table above shows statistics for 840 observations, covering average carbon trading prices and various economic indicators. The average transaction price of carbon trading is 32.80 yuan/ton, and the standard deviation is 23.46, indicating that the market price fluctuates significantly and may be affected by changes in policy and supply and demand. In terms of stock index, the average value of Shanghai Stock Index is 3102.76 and the standard deviation is 433.87, showing relatively stable market performance; while the average value of Shenzhen Index is 10946.09 and the standard deviation is as high as 2084.65, reflecting greater volatility. The energy index has a mean of 994.99 and a standard deviation of 263.93, indicating price volatility in the energy market.

In terms of raw material prices, the average price of raw coal is 438.05 yuan/ton, and the standard deviation is 266.85, indicating that the price fluctuates greatly. The average price of steel and iron ore is 3600.50 yuan and 477.64 yuan respectively, and the standard deviation is 886.67 yuan and 386.77 yuan respectively, reflecting the volatility of raw material market. The average price of LNG and gasoline is 4266.87 yuan and 3502.51 yuan respectively, and the standard deviation is 1479.23 yuan and 4052.17 yuan respectively, showing high fluctuation of energy prices. Nasdaq and Dow averages were 8604.20 and 25370.13, respectively, with standard deviations of 3568.57 and 6578.51, indicating significant volatility in the U.S. stock market.

V. Empirical Results

(a) Results of differential regression

The following tableshows the regression analysis results between various financial assets and macroeconomic factors in the seven major carbon trading markets in China. By comparing the regression coefficient, t value, standard error (Std) and coefficient of determination (R²) of different markets, we can observe the failure phenomenon of carbon trading market in pricing mechanism.

Table3Regression results of differential econometric model

Continued table 3:

The significance of regression coefficient reflects the influence degree of macro-economic factors on carbon trading market price. In Shenzhen market, the regression coefficient of Shanghai Stock Index is 0.000479, and the t value is 1.038654, which indicates that it has no significant effect on carbon trading price. In other markets, such as Beijing and Shanghai, the correlation coefficient is negative, and the t value is lower than the critical value, which further indicates that the relationship between prices and macroeconomic factors in these markets is weak. This phenomenon may reflect that the carbon trading market is not sensitive enough to macroeconomic fluctuations, resulting in the failure of the market pricing mechanism.

The coefficient of determination (R²) is generally low in all markets, especially in Tianjin and Chongqing, where R² values are close to zero, indicating that the model has limited explanatory power for carbon trading prices. This low explanatory power may be due to market participants 'lack of awareness of carbon trading, asymmetric information and imperfect market structure, resulting in market prices failing to effectively reflect the true supply-demand relationship.

Regression results for some markets show negative correlations between macroeconomic factors and carbon trading prices. For example, the raw materials index and the energy index show negative coefficients in several markets, suggesting that fluctuations in these factors may have a dampening effect on carbon trading prices. This phenomenon may be closely related to changes in the policy environment of carbon markets, the behavior patterns of market participants, and the external economic environment, further exacerbating market pricing failures.

At present, there are significant failures in the pricing mechanism of China carbon trading market, which are mainly reflected in the insignificant impact of macroeconomic factors on market prices, insufficient market interpretation ability and mismatch between price and supply and demand. This phenomenon suggests that policy makers and market participants need to strengthen supervision and guidance of carbon market, improve market transparency and participants 'awareness level, so as to promote the healthy development and effective pricing of carbon trading market.

Machine Learning Regression Results

In order to further explore the effectiveness of carbon pricing in the seven carbon trading markets, econometric forecasting models are reestablished by combining the influencing factors of carbon trading prices. In order to improve the forecasting accuracy of models and overcome the influence of different frequency data such as year, month and day, three machine learning forecasting models, decision tree, random forest and gradient elevator, are introduced on the basis of traditional econometric forecasting models. The MAE and RMSE predicted by this model are compared with those predicted by traditional models, and scientific and effective suggestions for carbon pricing in seven carbon trading markets are put forward.

In different regions (Shenzhen, Shanghai, Beijing, Guangdong, Tianjin, Hubei, Chongqing), by comparing the traditional linear regression model with three machine learning models (decision tree, random forest, gradient lift machine), it can be seen that the machine learning model is significantly better than the traditional linear regression model in predicting the carbon trading price.

Table4Comparison of decision tree prediction model with traditional linear regression

Table 4

Overall, all machine learning models exhibit lower error values on both MAE and RMSE metrics, indicating greater predictive power. For example, in Shenzhen, the MAE of the decision tree is 7.97 and RMSE is 11.53, which is significantly lower than the MAE (11.47) and RMSE (14.56) of traditional linear regression, and the accuracy is improved by 30.55% and 20.83%. Similar trends have been confirmed in other regions, especially in Shanghai and Guangdong, where machine learning models perform particularly well.

After comparing the MAE and RMSE of carbon trading markets in various regions, the regions with the most serious problems in market operation mechanism can be identified. Tianjin and Chongqing performed particularly well, showing larger MAE and RMSE values of 7.23 and 12.31, and 8.76 and 14.07, respectively. These high error indicators indicate that there are significant uncertainties and volatility in the price prediction of carbon trading markets in these two regions,indicating that there are many imperfect aspects of the operating mechanism of these two markets, which need to be further improved.

Among the three machine learning models, the gradient hoist performs best. In many regions, the MAE and RMSE of gradient hoist are lower than other models. For example, in Shenzhen, the MAE of the gradient hoist is 5.75, the RMSE is 7.86, and the accuracy improvement is 49.89% and 46.01%, respectively. This trend is also evident in Shanghai and Guangdong, showing that gradient hoists have a stronger ability to capture complex patterns in the data.

3) Importance of Eigenvalues

Among all machine learning models, the Gradient Boosting Machine (GBM) shows the most excellent performance and has become an effective tool for carbon pricing prediction. In order to further explore the important factors affecting carbon pricing and further reduce pricing errors, it is necessary to show the eigenvalues of gradient hoists in each region in detail. This process will help identify and analyze the extent to which each feature contributes to model predictions, thereby revealing key drivers that influence carbon trading price volatility.

Table5Ranking of Importance of Eigenvalues in Different Regions

Table 5

After analyzing the eigenvalues of gradient elevator in different regions, we can observe that there are significant differences in key factors affecting carbon pricing prediction in different regions, reflecting the uniqueness of regional markets and their sensitivity to carbon pricing. For example, carbon pricing in Shenzhen is mainly influenced by LNG prices and steel prices, showing its high sensitivity to energy price fluctuations, while bond yields are the main influencing factor in Shanghai, indicating the significant role of financial markets in carbon pricing. Beijing and Guangdong are also affected by bond yields and crude oil prices, reflecting the dependence of traditional energy prices on the market. Carbon pricing in Tianjin is closely related to industrial indices and crude oil prices, suggesting that we should pay attention to the impact of industrial activities on energy demand. Carbon pricing in Hubei and Chongqing is also influenced by both financial markets and energy prices, underscoring the importance of market sentiment and energy price volatility. Therefore, future carbon pricing strategies should focus on energy prices, financial indicators and industrial activities according to the characteristics of different regions, so as to improve the accuracy of forecasts, reduce pricing errors and promote the healthy development of carbon markets.

VI. Robustness test

5-fold cross-validation

In this study, a data partition method of training, validation and testing was adopted, and the last year in the sample was used as thetest set^[10]. For each algorithm,this paperuses five-fold cross-validation method to construct machine learning model, and uses set aside to evaluate the actual validity of the model. Five-fold cross validation is a resampling technique widely used in machine learning to estimate the performance of models on limited data samples.

Specifically,the observations in the cross-validation sample are randomly divided into five equal-sized subsets. Each subset is in turn used as a validation set, and the remaining four subsets are combined into a training set. The model is built on the training set and evaluated on the validation set using multiple evaluation metrics. A comprehensive assessment of model performance is generated by averaging the results of five validations. Therefore, all observations are used for training and validation, and each observation is used only once as validation data.

The model built from the cross-validation process is then applied to the test set after the training and validation periodsto generate loss estimates for that period. Figure 1 shows how these data are divided. It is worth noting thatobservations from the test set were not involved in the model development process. Therefore, thetest setis used only for final evaluation andnot as a criterion for model selection.

Figure1Five-fold cross validation diagram

In this paper, the carbon trading prices of 2021,2022 and 2023 are used as validation sets, and the training sets are divided into three time periods of 2014- 2020,2014 -2021 and 2014-2022 respectively, so as to predict the carbon trading prices of each year. By comparing the mean absolute error (MAE) and root mean square error (RMSE) of the prediction results, the experimental results can be considered robust if the prediction results agree with the experimental results described above. This methodology is designed to assess the predictive power of the model over different time periods to ensure its reliability and validity in practical applications.

(ii) Robustness test results

Table6Verification Results of Five-fold Price Difference

From the results of five-fold cross-validation, we can see that theexperimental results show good robustness. Random forest and gradient hoist showed significant accuracy improvements over traditional linear regression in many regions, especially in Shenzhen and Shanghai, where the accuracy improvements reached 48.87% and 63.37%, respectively. In addition, Guangdong and Hubei regions also showed higher accuracy improvement, especially the MAE and RMSE of random forest and gradient hoist were significantly lower than those of traditional linear regression, reaching 74.37% and 74.73% respectively. These results show that the selected model has strong adaptability and prediction ability when dealing with data from different regions, and reflects the robustness of the model as a whole.

VII. Conclusions and recommendations

Based on the data of China's seven carbon trading markets from 2014 to 2023, this paper analyzes the impact of macroeconomic factors on carbon trading prices, and uses machine learning methods to analyze the pricing problems of carbon trading markets. The results show that there is a significant negative correlation between macroeconomic factors and carbon trading price, and the traditional linear regression model is affected by data frequency and other factors when predicting carbon trading price, resulting in inaccurate prediction results. By introducing machine learning models such as decision tree, random forest and gradient elevator, the accuracy of carbon trading price prediction is significantly improved, especially in the analysis of market characteristics in different regions, the key factors affecting carbon pricing in different regions are revealed.

This paper provides some reference for controlling the imbalance of carbon trading market system and optimizing carbon pricing model. First,strengthen regional collaboration and policy coordination. When promoting low-carbon economic transformation, all regions should fully realize the spatial spillover effect of energy consumption on regional low-carbon transformation. In order to realize the low-carbon transformation of regional economy, it is necessary to formulate precise policies according to local conditions in combination with the characteristics of the region. At the same time, overall consideration shall be given to industrial chain coordination, industrial layout, energy production and consumption, cooperation with surrounding areas shall be strengthened, and interval linkage mechanism shall be established to avoid negative impact caused by spatial spillover effect of energy consumption among regions. Second,optimize the energy consumption structure. All regions should attach importance to the role of carbon trading pilot policies in promoting low-carbon transformation, reasonably control the total energy consumption in their regions, and optimize the energy consumption structure. Through scientific formulation of supporting policies, guide enterprises to strengthen independent innovation of energy utilization technology, gradually offset the increased cost of participating in carbon market exchanges, so as to realize the transformation of regional low-carbon economy. Third,enhance market transparency and supervision. In order to promote the healthy development of carbon trading market, policy makers should strengthen the regulation of carbon market, improve market transparency, ensure information symmetry, and reduce the possibility of market manipulation. By establishing sound market mechanisms and enhancing the trust of market participants, the efficiency of the carbon trading market will be further improved. Fourthly,advanced technology should be used to enhance forecasting capabilities. It is recommended that policy makers and market participants use advanced technologies such as machine learning to improve the prediction capabilities of carbon trading prices. This not only helps to better understand market dynamics, but also provides a scientific basis for policy adjustments and market decisions.

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