Multifractal Cross-Correlation Analysis of Carbon Emission Markets Between the European Union and China: A Study Based on the Multifractal Detrended Cross-Correlation Analysis and Empirical Mode Decomposition Multifractal Detrended Cross-Correlation Analysis Methods

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

Comment 1: The citation format is incorrect. "effects11", "volatility15", "dependence135", "(Zhu et al., 20197)", "(Yu et al, 202417)",...
Comment 2: Line 187 should be revised to R_t
Comment 3: Equation numbers are missing throughout the manuscript.
Comment 4: The "EU / A" in Table 1 is not visually clear.
Comment 5: Lines 227 and 231 should be revised to H_xy(2).
Comment 6: The descriptions for Figures 3, 4, and 7 are insufficient.
Comment 7: The font size in the figures is too small overall.
Comment 8: It would be helpful to highlight the differences between Figures 6 and 7 in the captions or titles. Terms like "shuffled" and "surrogate" should be included.

Comments on the Quality of English Language

Comment 9: Please check for any typos overall.
"The analyses of this study clarify the internal relationship", "and asymmetry of major carbon emission markets"

Author Response

We greatly appreciate the constructive feedback provided for our article and have diligently incorporated the suggested revisions. Considering your valuable comments, we have made the following adjustments. These changes aim to enhance the overall quality and clarity of the manuscript. Once again, we are grateful for your insightful comments and guidance in refining our work.

 

Comments 1: The citation format is incorrect. "effects11", "volatility15", "dependence135", "(Zhu et al., 20197)", "(Yu et al, 202417)",...

Response 1: Thank you for pointing this out. We agree with this comment. Therefore, after modifying the citation format of the references according to the journal template, we have changed "effects[11]", "volatility[15]", "dependence[13][5]", "model (Zhu et al., 2019[7])", "Prophet-EEMD-LSTM (Yu et al, 2024[17])" by "effects [1]", "volatility [2]", "dependence [3,4]", "model [7]", "Prophet-EEMD-LSTM [8]". Please see page 2, lines 60, 61 and 86.

Additionally, according the journal template, we have revised the format of all references and their citation format. All changes have been marked in red in the revised manuscript.

 

Comments 2: Line 187 should be revised to R_t.

Response 2: Thank you for pointing this out. We agree with this comment. Therefore we have replaced "R" to "R_t". Please see page 5, line 220.

 

Comments 3: Equation numbers are missing throughout the manuscript.

Response 3: Thank you for pointing this out. We agree with this comment. Therefore, we have added equation numbers to all the equations in the manuscript. Please see pages 3-5.

 

Comments 4: The "EU / A" in Table 1 is not visually clear.

Response 4: Thank you for pointing this out. We agree with this comment. Therefore we have replaced "EU / A" to "EUA". Please see page 6, Table 1.

 

 

Comments 5: Lines 227 and 231 should be revised to H_xy(2).

Response 5: Thank you for pointing this out. We agree with this comment. Therefore we have replaced "H_xy(q)" to "H_xy(2)". Please see page 7, lines 266 and 271.

 

Comments 6: The descriptions for Figures 3, 4, and 7 are insufficient.

Response 6: Thank you for pointing this out. We agree with this comment. Therefore we have enhanced the description and analysis of Figure 3, 4 and 7.

For Figures 3 and 4, Our analysis mainly focuses on the nonlinearity of h_q and τ_q. We have changed "From Figures 3 and 4, it is evident that both the Chinese and EU carbon emission markets exhibit nonlinear variations, further confirming the presence of multifractal characteristics between the two markets."

to

"As demonstrated in Figure 3 and Figure 4, the H_xy(q) and τ_q derived from the MF-DCCA and EMD-MF-DCCA methods both manifest non-linear characteristics irrespective of the value of q. This further indicates the presence of multiple fractal characteristics between the Chinese and EU carbon markets. Specifically, under the MF-DCCA model, the nonlinearities of H_xy(q) and τ_q of GD-EUA are more pronounced, while under the EMD-MF-DCCA model, the nonlinearities of H_xy(q) and τ_q of HB-EUA are more pronounced. This also indicates that the cross-correlation of returns between the Guangdong and EU carbon emission markets exhibits stronger fractality in long-term trends, whereas the cross-correlation between the Hubei and EU carbon emission markets demonstrates stronger fractality in short-term fluctuations."

Please see page 9, lines 310-319.

 

Additionally, the analysis of Δh has been moved above Table 2. For the relationship between the H_xy(q) and 0.5, we have added a detailed analysis in this part, which is as follows:

"Furthermore, when q is small, the H_xy(q) of GD-EUA and HB-EUA are greater than 0.5. In contrast, when q is large, the H_xy(q) of GD-EUA and HB-EUA are smaller than 0.5. Hence, for the Chinese and EU carbon emission markets, the persistence characteristics are displayed in the small fluctuations’ behaviour of return series, while the larger fluctuations of return series are anti-persistent."

Please see page 7, lines 275-280.

 

With regard to Figure 7, we have made a concrete analysis together with Table 3, Figures 5 and 6, and have replaced

"Table 3, Figures 6, and 7 present a detailed comparison of the Hurst exponent and multifractal spectra of the carbon emission allowance returns in the Chinese and EU carbon emission markets. Then we found that the multifractality in both markets is primarily attributed to fat-tailed distributions. Specifically, by comparing the data in Figure 6 and Table 3, we observe that the generalized Hurst exponent h(q) for both shuffled and surrogate sequences of the two return series varies with changes in the q values. Moreover, the multifractal strength Δh of the surrogate sequences is generally lower than that of the original sequences, indicating that fat-tailed probability distributions are a key factor contributing to multifractality. The shuffled sequence's multifractal strength (Δh) for the GD-EUA sequence is less than that of the original sequence, indicating the contribution of long-range correlations to the series' multifractality. Based on the above analysis, we found that compared with the long-range correlation, the influence of thick-tailed distribution on multifractal is more significant, which is just in line with the width of the multifractal map shown in the Figure 6."

to

"Table 3 and Figures 5-7 present a detailed comparison of the Hurst exponent and multifractal spectra of the carbon emission allowance returns in the Chinese and the EU carbon emission markets. Then the study finds that, compared to the original sequence, the Δh of the shuffled and surrogate sequences of GD-EUA is reduced, while the changes in Δα are very small. For HB-EUA, both Δh and Δα decrease noticeably, except that the Δh of the surrogate sequence derived from the MF-DCCA method increases slightly. These findings indicate that both fat-tailed probability distributions and long-range correlations contribute to the multifractality of returns in the Chinese and EU carbon emission markets, with the effect being particularly pronounced for the cross-correlation between the Hubei and EU carbon emission markets."

   Please see pages 10 and 11, lines 357-367.

   

Comments 7: The font size in the figures is too small overall.

Response 7: Thank you for pointing this out. We agree with this comment. Therefore the font size of all figures in the revised manuscript has been increased. Please see Figure 1 to Figure 8.

 

Comments 8: It would be helpful to highlight the differences between Figures 6 and 7 in the captions or titles. Terms like "shuffled" and "surrogate" should be included.

Response 8: Thank you for pointing this out. We agree with this comment. Consequently, we have updated the title of Figure 6 to "Multiple Fractal Spectra of HB-EUA, GD-EUA Cross-Correlation for Shuffled Sequences." Additionally, the title of Figure 7 has been revised to "Multiple Fractal Spectra of HB-EUA, GD-EUA Cross-Correlation for Surrogate Sequences." Please see page 11, Figure 6; page 12, Figure 7.

 

Comments 9: Please check for any typos overall.

"The analyses of this study clarify the internal relationship", "and asymmetry of major carbon emission markets"

Response 9: Thank you for pointing this out. We agree with this comment. Therefore we have changed "The analyses of this study clarifies the internal relationship" to "This study clarifies the internal relationship". Please see page 2, line 53.

"and asymmetry of major carbon emission markets in China and the European Union " has also been changed to "asymmetry of volatility in the main Chinese carbon emission markets and the EU carbon emission market". Please see page 3, line 97 and 98.

Additionally, we have carefully checked the spelling and grammar in the manuscript. All identified errors have been corrected in the revised manuscript.

 

Author Response File: Author Response.docx

Reviewer 2 Report

Comments and Suggestions for Authors

Please see the attached file.

Comments for author File: Comments.pdf

Author Response

We are very grateful for your detailed comments on our paper and agree to accept it without any changes. We have also carefully revised the paper, taking into account the comments from the other three reviewers. These changes aim to enhance the overall quality and clarity of the manuscript. Once again, we are grateful for your review.

Reviewer 3 Report

Comments and Suggestions for Authors

Authors present the MFDCCA method . If they present a comparison of results between  MFDCCA and  EMD-MF-DCCA it will improve the quality of the paper

with this modification paper can be accepted

Author Response

We greatly appreciate the constructive feedback provided for our article and have diligently incorporated the suggested revisions. Considering your valuable comments, we have made the following adjustments. We are greatly inspired by the important studies you recommended and have made great improvements in the manuscript. These changes aim to enhance the overall quality and clarity of the manuscript. Once again, we are grateful for your insightful comments and guidance in refining our work.

 

Comments 1: Authors present the MF-DCCA method. If they present a comparison of results between MF-DCCA and EMD-MF-DCCA, it will improve the quality of the paper. With this modification paper can be accepted.

Response 1: Thank you for pointing this out. We agree with this comment. Therefore we have applied the EMD-MF-DCCA model to this paper. The model has been incorporated into Section 3.3 on page 5, and the corresponding results have been added in Figure 2 to Figure 8, as well as Table 2 and Table 3.

By comparing the results obtained from the MF-DCCA model and the EMD-MF-DCCA model, a significant cross-correlation between the returns of the Chinese and the EU carbon emission markets is identified, along with the presence of multifractal characteristics. Furthermore, it was found that the cross-correlation between the returns of the Guangdong and the EU carbon emission markets demonstrates a stronger degree of multifractality in the long-term trends, while the cross-correlation between the Hubei carbon market and the European Union carbon market exhibits stronger multifractality in short-term fluctuations. Regarding the underlying causes of the fractality, the results indicate that both fat-tail distributions and long memory contribute to the fractality of cross-correlation between the Chinese and EU carbon emission markets, with a particularly significant impact on the fractality observed between the Hubei and EU carbon emission markets. For the above conclusions and corresponding analyses, we have made relevant modifications in the revised manuscript. Please see page1, Abstract and Keywords; pages 7-11, the analysis marked in red; pages 13, lines 433 and 434; page 14, lines 435, 436, 439-441.

 

In addition, in response to the newly added conclusions, the first suggestion has been expanded. Specifically, we have changed

"Additionally, China must strengthen the regulatory capacity of its institutions, implement effective market supervision, and manage risks to provide a stable operating environment for the carbon emission market. Such measures would not only enhance market efficiency but also boost investor confidence, attracting more capital into the market."

to

"Additionally, China must strengthen the regulatory capacity of its institutions, implement effective market supervision, and manage risks, with particular focus on the short-term fluctuation risks in the Hubei carbon emission market. These measures are crucial for providing a stable operational environment for the carbon emission markets. Not only will they improve market efficiency, but they will also strengthen investor confidence, thereby attracting more capital into the market."

   Please see page 14, lines 465-471.

Author Response File: Author Response.docx

Reviewer 4 Report

Comments and Suggestions for Authors

The article is devoted to the study of the special relationship between carbon emission in comparison of the European Union and China.  The relevance of the study is based on the importance of meeting the Kyoto Protocol targets for reducing carbon dioxide emissions (carbon emission). It is also important to observe the carbon emission of developing countries because modern manufacturing is most often located in developing countries. Even though China is now a developed country, there is some correlation between the number of manufactures, exporting countries, and shipping routes. In this case, the authors have chosen to study the European Union countries as a carbon dioxide emitting system in aggregate.

As a result, dependencies of the coefficient τ on the value of q are presented, as well as a set of logarithmic yield curves of the Chinese market and the carbon emissions of the European Union. The oscillation curves have a generally linear character, which confirms the presence of significant cross-correlation. The most important merit of the paper is the practical recommendations that the Chinese carbon market further reduce carbon trading fees and introduce tax credits and other incentives.

There are various errors in the text in English. In this vein, it is a bit unclear why the abstract presents a certain "Chinese China Carbon....   ", however, it can be corrected at the proofreading stage.

Author Response

We greatly appreciate the constructive feedback provided for our article and have diligently incorporated the suggested revisions. Considering your valuable comments, we have made the following adjustments. These changes aim to enhance the overall quality and clarity of the manuscript. Once again, we are grateful for your insightful comments and guidance in refining our work.

 

Comments 1: There are various errors in the text in English. In this vein, it is a bit unclear why the abstract presents a certain "Chinese China Carbon....", however, it can be corrected at the proofreading stage.

Response 1: Thank you for pointing this out. We agree with this comment. Therefore we have changed "Chinese China Carbon...." to "Chinese Carbon....". Please see page 1, line 26, 27.

Additionally, we have carefully checked the spelling and grammar in the manuscript. All identified errors have been corrected in the revised manuscript.