Fluctuations and Forecasting of Carbon Price Based on A Hybrid Ensemble Learning GARCH-LSTM-Based Approach: A Case of Five Carbon Trading Markets in China

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

L10: Include quantitative data in the abstract, such as specific forecast results for carbon prices in five markets and the R2 value achieved by the GARCH-LSTM model.

L12: Define all acronyms in full when they first appear.

L14: Explain the choice of LSTM over other machine learning models. Were preliminary experiments conducted to support this decision??

L35-38: Please add references to support these sentences.

L63: Please explain the meanings of 'volatility clustering' and 'long-term memory characteristics.'

L70: Please explain the meaning of 'Short-term memory characteristics.'

L71: Revise the informal reference style from 'Kainuma (1999) and others' to a formal citation format. Ensure Kainuma's work is included in the bibliography. Also, if different models yield different carbon prices in the same market, which one is reliable?

L86: This statement about the RNN's predictive performance contradicts the earlier assertion in L52.

L89: Please provide specific predictive results for CNN.

L132: Why not use LSTM-IWOA for prediction?

L135: Many studies have adopted the GARCH-LSTM model for prediction, including for carbon price forecasting (https://doi.org/10.1016/j.apenergy.2021.116485). Please clarify the differences from these studies.

L57-137: Condense these two paragraphs and concisely summarize the literature review findings.

L140-142: Clarify the terms 'volatility characteristics' and 'fluctuations,' highlighting their differences.

L148-152: The conclusion should directly address these three questions

L165: Justify the selection of GARCH, GARCH-M, and TGARCH models for your study.

L229: Include a section explaining the principles behind the GARCH-LSTM model.

L231: Add references for the information regarding China's eight carbon emission markets.

L243: In Table 1, what is the difference between 'Total trading volume' and 'Total trade volume.' Provide references for the Data Source: Carbon Trading Centers.

L325: Explain the purpose of the 4.2 Stationarity Test.

L363: Detail the differences between the GARCH(1,1), GARCH(2,1), and GARCH(1,2) models.

L493: Include the R2 metric in Table 9 for a comprehensive analysis.

L530: With a significant difference between the forecast and actual lines for Hubei, how credible are the results? What should be done if someone want to predict for Hubei?

Figures: All figures must be modified with clear visions, axes names, units, and legends, e.g., Figure 10 is very hard to distinguish GD and GDF.

Comments on the Quality of English Language

Define all acronyms in full when they first appear.

Author Response

Dear Editors and Reviewers of Sustainability:

Thank you very much for taking your time to review my manuscript. I really appreciate all your decision and constructive comments on my manuscript. We have carefully considered the suggestion of Reviewer and make some changes. We have tried our best to improve and made some changes in the manuscript. According to your comments, we have revised my manuscript accordingly and marked it with red font. The detailed explanation of the point-to-point revision as follows:

Reply Reviewer #1:

 

1. L10: Include quantitative data in the abstract, such as specific forecast results for carbon prices in five markets and the R2 value achieved by the GARCH-LSTM model.

Thank you for your suggestions. Corresponding changes have been made in the abstract. Shown in L21-27.

2. L12: Define all acronyms in full when they first appear.

Thank you for your suggestions. It has been modified and identified accordingly in the text. Shown in L193, L207, L224 and L246.

3. L14: Explain the choice of LSTM over other machine learning models. Were preliminary experiments conducted to support this decision?

Thank you for your suggestions. The results of the LSTM combination model in other scholars' existing studies have been compared with the mean square error results of a single traditional econometric model (such as GARCH model) and machine learning (such as BP model, LSTM model, etc.), and the preliminary experiments support the GARCH-LSTM model to predict more accurately, as detailed in L566-L579.

4. L35-38: Please add references to support these sentences.

Thank you for your suggestions It has been modified and identified in the text. Shown in L41.

5. L63: Please explain the meanings of 'volatility clustering' and 'long-term memory characteristics.'

Volatility concentration shows that the price yield of the carbon trading market fluctuates around the mean value. If the yield rate is small in a certain period, the yield rate will continue to decrease in the next period. Or if the rate of return is large in a certain period of time, the rate of return continues to increase in the next period of time, and there is volatility accumulation. The characteristics of long-term memory mean that the impact of bad news and good news in the carbon market will last for a long time, and it will last for a long time after the impact, and its impact is difficult to eliminate in a short time, which will have an impact on future fluctuations.

6. L70: Please explain the meaning of 'Short-term memory characteristics.'

Short-term memory features that prices are not random walks, and historical price information is not fully reflected in current carbon prices.

7. L71: Revise the informal reference style from 'Kainuma (1999) and others' to a formal citation format. Ensure Kainuma's work is included in the bibliography. Also, if different models yield different carbon prices in the same market, which one is reliable?

(1) Kainuma's bibliographic reference citation format has been changed to an official citation format, and its literature has been added to the bibliography.

(2) If different models generate different carbon prices in the same market, it is necessary to confirm the size of the error between the actual and predicted results, and calculate the accuracy of the prediction results, and the model with high accuracy is relatively reliable.

8. L86: This statement about the RNN's predictive performance contradicts the earlier assertion in L52.

Thank you for your suggestions. It has been modified.

9. L89: Please provide specific predictive results for CNN.

Thank you for your suggestions. It has been modified.

10. L132: Why not use LSTM-IWOA for prediction?

Because both the LSTM-IWOA model and the GARCH-LSTM model used in this paper belong to LSTM models, the prediction accuracy is high, but the two are fundamentally different. The former IWOA is an optimization algorithm, which optimizes the LSTM model through the IWOA method, reduces and avoids the prediction bias of the LSTM model caused by human experience differences, and improves the convergence speed and prediction accuracy of the optimized model. The latter GARCH is an econometric model, which combines the traditional model with machine learning methods, and uses the advantages of the LSTM model to predict data with long feature interval and long delay to learn GARCH sequence features and improve the prediction performance of the model.

11. L135: Many studies have adopted the GARCH-LSTM model for prediction, including for carbon price forecasting. Please clarify the differences from these studies.

Bi LSTM (bidirectional long short-term memory) is the process of making any neural network have sequential information in both backward (future-to-past) or forward (past-to-future) directions. BP and LSTM are both neural network methods, and LSTM is superior to BP network method in terms of time series and sequence data processing and analysis

12. L57-137: Condense these two paragraphs and concisely summarize the literature review findings.

Thank you for your suggestions. It has been modified in the text, as detailed in paragraphs 4 to 7 of Part I. Based on the different types of prediction models, this paper reviews the literature of scholars and discusses the price prediction of carbon trading in China from three aspects: one is to use traditional econometric methods to predict carbon prices, the other is to predict carbon market prices based on single models such as neural networks and machine learning, and the third is to use a combination of the above two methods to predict carbon market prices. The results of the literature review are also briefly elaborated.

13. L140-142: Clarify the terms 'volatility characteristics' and 'fluctuations,' highlighting their differences.

Thank you for terms suggested. The terms 'volatility characteristics' and 'fluctuations' are used to describe the fluctuation of carbon trading prices and their characteristics, and there is basically no difference between these two.

14. L148-152: The conclusion should directly address these three questions

Thank you for your suggestions. Three issues have been addressed in the conclusion. See L643-L682 for details.

15. L165: Justify the selection of GARCH, GARCH-M, and TGARCH models for your study.

In 2.1, 2.2 and 2.3, the rationality of GARCH, model, GARCH-M, model and TGARCH model is explained in 2.1, 2.2 and 2.3 respectively, which have been identified. Shown in L184-192, L194-196, L208-210, L219-223, L225-230, L241-245 for details.

16. L229: Include a section explaining the principles behind the GARCH-LSTM model.

Thank you for your suggestions. It has been modified and identified in the text. Shown in L247-261 and L279-285 for details.

17. L231: Add references for the information regarding China's eight carbon emission markets.

Thank you for your suggestions. It has been added and identified in the text. Shown in L290-296 for details.

18. L243: In Table 1, what is the difference between 'Total trading volume' and 'Total trade volume.' Provide references for the Data Source: Carbon Trading Centers.

Thank you for your suggestions. It has been modified and identified in Figure 1. The first column is the total trading volume, and the third column is the total transaction volume.

19. L325: Explain the purpose of the 4.2 Stationarity Test.

Thank you for your suggestions. The purpose of explaining stationarity testing has been added and identified in 4.2. The purpose of stationarity test is to ensure the stability of time series data through stationarity test in order to avoid possible statistical problems such as pseudo-regression as much as possible in the process of modeling and analysis, that is, the statistical properties of the data remain unchanged at different time points. Explanations have been made accordingly. Shown in L389-392 for details.

20. L363: Detail the differences between the GARCH(1,1), GARCH(2,1), and GARCH(1,2) models.

A higher-order GARCH model can contain any number of ARCH items and GARCH items, denoted as GARCH(p, q), where p is the order of the ARCH item and q is the order of the GARCH item, for example, GARCH(1,1) in this article means that the GARCH model contains the first-order ARCH term and the first-order GARCH term.

21. L493: Include the R2 metric in Table 9 for a comprehensive analysis.

Thank you for the Table suggested. The R2 metric for a comprehensive analysis has added in Table 9. Shown in L567.

22. L530: With a significant difference between the forecast and actual lines for Hubei, how credible are the results? What should be done if someone want to predict for Hubei?

Thank you for your suggestions. It has been explained and identified in the text. The main reasons for the error between the prediction line and the actual line of the Hubei carbon trading market are that: (1) due to the influence of China's economic macro factors, the carbon trading price shows some abnormal fluctuations, and the actual value has individual outliers, for example, the prediction error of the Hubei forecast results is small in the first 260 sample data, and relatively large after that, that is, after February 28, 2022, macro factors are external factors affecting the fluctuation of carbon trading prices. Including economic, political, social factors, as well as natural environmental conditions, etc., macro factors are complex and difficult to quantify, and relevant information is not included in the prediction model. (2) Compared with other prediction charts, Fig. 12 has a smaller scale interval (0.1), which makes the difference between the predicted value curve and the actual value curve more significant. At the same time, existing studies have failed to solve this problem. In order to better solve this problem, the prediction model of high-dimensional macro information is considered to see whether the prediction accuracy can be further improved.

23. Figures: All figures must be modified with clear visions, axes names, units, and legends, e.g., Figure 10 is very hard to distinguish GD and GDF.

Thank you for the Figures suggested. All figures have been modified.

 

It should be noted that due to the appropriate condensation of this part of the content according to the comments of the reviewers, the original relevant content covered by questions 6, 8 and 9 has been deleted.

In addition, we apologize for the poor language of our manuscript. We worked on the manuscript for a longtime and the repeated addition and removal of sentences and sections obviously led to poor readability.

We have now worked on both language and readability and have also involved native English speakers for language corrections. We really hope that the flow and language level have been substantially improved.

We would love to thank you for allowing us to resubmit a revised copy of the manuscript and we highly appreciate your time and consideration.

Sincerely,

Liu Sha

Author Response File: Author Response.docx

Reviewer 2 Report

Comments and Suggestions for Authors

The research is relevant mainly due to the considerations of models and frameworks used to analyze the persistence, risk and asymmetry of the price and yield volatility of the cable trade. This manuscript may be relevant for its publication, but the authors should provide more details about the structure and organization of the article.
the introduction is vast and does not have a topic on the theoretical foundation, I suggest better balancing the introduction and creating a topic on the theoretical foundation.
The methodology discusses the models used, but does not present the scientific methods or methodological procedures of how the experiment or the empirical part was carried out, preventing the reproduction of the findings.
The results topic is very detailed.

Author Response

Dear Editors and Reviewers of Sustainability:

Thank you very much for taking your time to review my manuscript. I really appreciate all your decision and constructive comments on my manuscript. We have carefully considered the suggestion of Reviewer and make some changes. We have tried our best to improve and made some changes in the manuscript. According to your comments, we have revised my manuscript accordingly and marked it with red font. The detailed explanation of the point-to-point revision as follows:

Reply Reviewer #2:

1.The research is relevant mainly due to the considerations of models and frameworks used to analyze the persistence, risk and asymmetry of the price and yield volatility of the cable trade. This manuscript may be relevant for its publication, but the authors should provide more details about the structure and organization of the article.

Thank you for your suggestions. More details about the structure and organization of the article are provided as follow, the first section reviews the current research status and theories of carbon trading market price fluctuation and prediction literature, and puts forward the research content and objectives of this paper. The second section proposes the model and method selected in this paper on the basis of the existing literature research, that is, the GARCH-LSTM model which combines the traditional econometric model and intelligent machine learning. The third section elaborates the source of data used in this study, data processing and the basic situation of China's five carbon trading pilot markets. The fourth section carries out empirical analysis, using GARCH family model to analyze the volatility, risk and asymmetry of the change of carbon trading price return time series, and using GARCH-LSTM model to predict carbon trading price and measure the prediction accuracy of the model. The fifth section summarizes the main research conclusions according to the research objectives, and puts forward corresponding policy recommendations.

2.The introduction is vast and does not have a topic on the theoretical foundation, I suggest better balancing the introduction and creating a topic on the theoretical foundation.

Thank you for your suggestions. The introduction has been revised, and according to the introduction, the theme of this paper and the problems to be solved. Shown in L61-182 for details.

3.The methodology discusses the models used, but does not present the scientific methods or methodological procedures of how the experiment or the empirical part was carried out, preventing the reproduction of the findings.

The proposed experiment is interesting and could provide additional information relevant to the model science method or methodological procedure of this study, but we consider it to be outside the scope of this study. In fact, this study has combined actual data from five carbon trading markets in China to conduct a detailed operation of the scientific method or methodological procedure on how to conduct the experimental or empirical part. Shown in the fourth part of this study for details.

 

In addition, we apologize for the poor language of our manuscript. We worked on the manuscript for a longtime and the repeated addition and removal of sentences and sections obviously led to poor readability.

We have now worked on both language and readability and have also involved native English speakers for language corrections. We really hope that the flow and language level have been substantially improved.

We would love to thank you for allowing us to resubmit a revised copy of the manuscript and we highly appreciate your time and consideration.

 

Sincerely,

Liu Sha

Author Response File: Author Response.docx

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

Some comments in the first round review were no addressed:

Comment 2: The previously mentioned suggestion remains unaddressed. For instance, ADF and ARCH. Please read a published paper.

Comment 3: L566-L579 did not explain this.

Comment 4: This reference (Chen and Xing，2019) does not contain these data; please verify.

Comment 5-7, 20: For clarity and completeness, it would be beneficial to incorporate these explanations into the manuscript.

Comment 10: Yang et al.(2020) employs LSTM-IWOA to predict the carbon trading prices of Beijing, Fujian and Shanghai carbon markets. Why not use LSTM-IWOA for prediction in your study?

Comment 11: The response does not address my inquiry. It is crucial to explicitly articulate the novelty of this study, particularly in comparison to previous research.

Comment 13: Please ensure this uniformity in the revised paper.

Comment 16: The principles behind the GARCH-LSTM model should be explained, instead of the single LSTM model.

Comment 17-18: Please include the relevant website links or bibliographic references.

Figures: All the symbols in the figure should be provided with legend.

Comments on the Quality of English Language

I have no comments on the English quality of this paper.

Author Response

Dear Editors and Reviewers of Sustainability:

Thank you very much for taking your time to review my manuscript. I really appreciate all your decision and constructive comments on my manuscript. We have carefully considered the suggestion of Reviewer and make some changes. We have tried our best to improve and made some changes in the manuscript. The yellow part that has been revised according to your comments. According to your comments, we have revised my manuscript accordingly and marked it with red font. The detailed explanation of the point-to-point revision as follows:

 

1.Comment 2: The previously mentioned suggestion remains unaddressed. For instance, ADF and ARCH. Please read a published paper.

Thank you for your suggestions. The abbreviation that appears for the first time in the text has been fully defined.

2.Comment 3: L566-L579 did not explain this.

Thank you for your suggestions.

1）The reason for choosing the LSTM model is that the LSTM model can effectively solve the gradient vanishing problem, which can optimize the depth of the model and prevent the gradient problem, and at the same time, the LSTM model has the advantages of predicting data with long feature interval and long delay to learn sequence features, which improves the accuracy of prediction results.

2）This study does not conduct preliminary experiments to support this decision, but through a large number of literature readings, the results of scholars choosing the LSTM model for price prediction are sorted out, and this is used as a support for the decision to choose this model in this study. The decision process of this study is as follows: firstly, it is found that the price prediction by using the LSTM model can improve the prediction accuracy from the existing research. References such as: ①Peng L, Liu S, Liu R, et al. Effective long short-term memory with differential evolution algorithm for electricity price prediction [J]. Energy, 2018,162:1301-1314. (2) Song Gang, Zhang Yunfeng, Bao Fangxun, et al. Stock prediction model based on particle swarm optimization LSTM[J]. Journal of Beijing University of Aeronautics and Astronautics,2019,45(12):2533-2542.③Yang B,Sun S,Li J,et al. Traffic flow prediction using LSTM with feature enhancement[J].Neurocomputing,2019,332:320-327.

In addition, this study finds that the relevant research proves that the LSTM combination model can achieve a more accurate price prediction effect. References such as: ①Alameer Z, Fathalla A, Li K, et al. Multistep-ahead forecasting of coal prices using a hybrid deep learning model [J]. Resources Policy, 2020,65:101588.②Niu H, Xu K, Wang W. A hybrid stock price index forecasting model based on vibrational mode decomposition an-d LSTM network [J]. Applied Intelligence, 2020,50(12):4296-4309.

3.Comment 4: This reference (Chen and Xing，2019) does not contain these data; please verify.

Thank you for your suggestions. Modified and identified in the original text. SeeL41-43.

4.Comment 5-7, 20: For clarity and completeness, it would be beneficial to incorporate these explanations into the manuscript.

5.Comment 10: Yang et al.(2020) employs LSTM-IWOA to predict the carbon trading prices of Beijing, Fujian and Shanghai carbon markets. Why not use LSTM-IWOA for prediction in your study?

It is found that although the two types of combined models, LSTM-BP and LSTM-IWOA, can improve the accuracy of the prediction model, they do not fully consider the time series characteristics of the data in trend forecasting, and it is difficult to avoid the influence of feature redundancy on trend prediction. Therefore, this paper adopts the GARCH-LSTM combination model, and by incorporating features such as time series into the model, the disadvantages of the above model are well avoided, the influence of feature redundancy on trend prediction is solved, and the accuracy of the prediction results is improved. See L139-142 for details.

6.Comment 11: The response does not address my inquiry. It is crucial to explicitly articulate the novelty of this study, particularly in comparison to previous research.

The innovativeness of this study is crucial. From the analysis of the fluctuation characteristics of China's carbon trading price, it can be seen that the core of carbon trading price prediction is to deal with the complex fluctuation of carbon price over time. Therefore, this paper adopts the GARCH-LSTM combination model, and adds the GARCH family model coefficients containing sequence information to the input layer of the LSTM model, that is, the conditional heteroskedasticity of the time series of fluctuation aggregation and fluctuation persistence, asymmetric volatility, leverage effect, and enhanced asymmetric fluctuation flexibility are added to the prediction conditions, and the advantages of the LSTM model can predict data with long feature interval and long delay to learn the sequence features. It avoids the drawbacks of other combined models such as LSTM-BP, LSTM-RNN and LSTM-IWOA, solves the influence of feature redundancy on trend prediction, and significantly improves the prediction performance of the model. In addition, no scholar has used the GARCH-LSTM combination model to predict carbon trading prices, and this study has a certain degree of originality. See L149-157 for details.

7.Comment 13: Please ensure this uniformity in the revised paper.

Thank you for your suggestions. The terms 'volatility characteristics' and 'fluctuations' have been checked throughout to ensure consistency.

8.Comment 16: The principles behind the GARCH-LSTM model should be explained, instead of the single LSTM model.

Thank you for your suggestions. The rationale behind the GARCH-LSTM combination model is described in this study 2.5 and is detailed in L307-317.

9.Comment 17-18: Please include the relevant website links or bibliographic references.

Thank you for your suggestions. Relevant sources have been attached, see L340-346 for details.

10.Figures: All the symbols in the figure should be provided with legend.

After we checked again and again, the legend is missing from figures 2 to 6 in the paper. These charts are the price fluctuation trend charts of five typical carbon trading markets in China, in which the broken line represents the mean price of the carbon market, and the scattered point represents the actual price value of the carbon market on the trading day, and the legend has been added accordingly.

 

In addition, after the entire review, a number of spelling errors were found and corrected, which have been identified in red font in the text.

We have now worked on both language and readability and have also involved native English speakers for language corrections. We really hope that the flow and language level have been substantially improved.

We would love to thank you for allowing us to resubmit a revised copy of the manuscript and we highly appreciate your time and consideration.

 

Sincerely,

Liu Sha

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

The authors improve the organization and structure of the article, making several improvements. This way, the article can be accepted

Author Response

Dear Reviewer,

Thank you very much for your insightful comments and contributions to this manuscript! 

Round 3

Reviewer 1 Report

Comments and Suggestions for Authors

Given the nature of a scientific paper, it is beneficial for the final published version to delineate the distinctions between the present study and the work published at  https://doi.org/10.1016/j.apenergy.2021.116485, especially considering the similarity in their titles. Beyond this point, I have no additional comments.

Author Response

Dear Editors and Reviewers of Sustainability:

Thank you very much for taking your time to review my manuscript. I really appreciate all your decision and constructive comments on my manuscript. We have carefully considered the suggestion of Reviewer and make some changes. We have tried our best to improve and made some changes in the manuscript. The yellow part that has been revised according to your comments. According to your comments, we have revised my manuscript accordingly and marked it with red font. The detailed explanation of the point-to-point revision as follows:

Given the nature of a scientific paper, it is beneficial for the final published version to delineate the distinctions between the present study and the work published at https://doi.org/10.1016/j.apenergy.2021.116485, especially considering the similarity in their titles.

Thank you for your suggestions.

According to the reviewer's opinion, we have read the study of Huang et al. (2021), and the results show that the GARCH-LSTM model reduces the prediction error and improves the prediction accuracy, which is consistent with the results of this study. Huang et al. (2021) proposed a new disintegration-integration paradigm VMD-GARCH/LSTM-LSTM carbon price prediction model. The new model is divided into low-frequency sub-model and high-frequency sub-model, in which LSTM model is used to predict the low-frequency sub-model. The GARCH model predicts the high frequency sub-model. In this paper, the characteristics of GARCH model such as time series are incorporated into LSTM model, and the GARCH family model is used to explore the agglomeration, asymmetry and risk premium of carbon price fluctuations. Then, GARCH family model coefficients containing sequence information are added to the input layer of LSTM model, so as to predict carbon price. At the same time, the originality of this paper also lies in the use of GARCH-LSTM model to predict the future fluctuation of carbon price. Shown in L142-145, L152-162, and L803-804 for details.

We would love to thank you for allowing us to resubmit a revised copy of the manuscript and we highly appreciate your time and consideration.

Sincerely

Liu Sha

Author Response File: Author Response.pdf