Correction: Cheng, Y. Carbon Derivatives-Directed International Supervision Laws and Regulations and Carbon Market Mechanism. Sustainability 2022, 14, 16157

The author would like to make the following corrections about the published paper [1]. The changes are as follows:

(1)

Adding missing subfigure(a) in Figure 9:

Replacing the original version:

Figure 9. Sparse graph of the coefficient estimation matrix (Carbon Market Turnover Volume Weighted yield). Note: From left to right are Componentwise HVAR, lag-weighted Lasso and Lag Group. The sequence of variables in the figure is the same as above.

Figure 9. Sparse graph of the coefficient estimation matrix (Carbon Market Turnover Volume Weighted yield). Note: From left to right are Componentwise HVAR, lag-weighted Lasso and Lag Group. The sequence of variables in the figure is the same as above.

• with:

  Figure 9. Sparse graph of the coefficient estimation matrix. (a) Carbon Market trading volume Weighted yield. (b) Carbon Market Turnover Volume Weighted yield. Note: From left to right are Componentwise HVAR, lag-weighted Lasso and Lag Group. The sequence of variables in the figure is the same as above.

  Figure 9. Sparse graph of the coefficient estimation matrix. (a) Carbon Market trading volume Weighted yield. (b) Carbon Market Turnover Volume Weighted yield. Note: From left to right are Componentwise HVAR, lag-weighted Lasso and Lag Group. The sequence of variables in the figure is the same as above.

(2)

Adding explanation of Figure 9 in “Section 3”:

(before “On 16 July 2021”,): On the basis of Liu, Z et al. (2022) [24], this empirical study expanded the sample data size to more than one year, which improved the accuracy of the analysis after the launch of the National Carbon Market.

(After Figure 9) As can be seen from the above six figures, in most cases, variables have a positive impact on the industry return rate, and each variable also influences each other. With the change of the model, the influence degree of each variable varies greatly. In the Lag-weighted Lasso model, most variables have a certain degree of mutual influence, but the influence of the variables is gradually weakened. In the volume-weighted results, each energy variable has a relatively obvious influence, while the enterprise debt index has a relatively strong influence on most variables, and the coke and the exchange rate of USD against RMB has a relatively significant influence. In the HVAR model, there are significant influences between asphalt and coke and most of the variables, and most of the influences are positive. From the above results, it can be seen that in most cases, HVAR has a better impact on the significance of various variables and has a better impact on the significance of various variables and is better reflected.

Replacing the original version on page 10:

“the rise in the regional carbon emissions price will significantly increase the national level...Otherwise, there will be no positive spillover effect of rising energy prices leading to rising carbon emission rights prices.”

• with:

“It can be seen from the above tables that, when carbon emission weighted yield rate and national carbon yield rate data are introduced at the same time, thermal coal continuous and asphalt recent months will have a positive impact on the result, which has a certain effect on volume weighting, and asphalt futures also have a positive impact on the national carbon yield rate. So, the energy market has an impact on both the industry and all carbon revenue data. Additionally, relatively speaking, most of the other energy sources will have a positive impact on either the volume-weighted yield or the turnover-weighted yield, as well as the national carbon data yield.”

(3)

Replacing the sentences in “Section 3” on page 9:

In the empirical analysis before the operation of the National Carbon Market, the order of variables is volumeweighted yield (transaction volume-weighted yield), industry-weighted yield, CSI300, steam coal continuous, asphalt recent, fuel recent, coke recent, crude oil recent, overnight Shanghai Interbank Offered Rate (SHIBOR), national debt index, corporate debt index, and dollar to dollar/RMB exchange rate by China Foreign Exchange Trade System (CFETS). In the empirical analysis after the launch of the National Carbon Market, yield data of the National Carbon Market are put after the “Carbon Market turnover-weighted yield(turnover-weighted yield)”.

• with:

In the empirical analysis after the operation of the National Carbon Market, the order of variables is Carbon Market volume weighted yield (turnover weighted yield), industry-weighted yield, CSI300, corporate debt index, steam coal continuous, crude oil recent, national debt index, asphalt recent, coke recent, fuel recent, dollar to RMB exchange rate by China Foreign Exchange Trade System (CFETS) and overnight Shanghai Interbank Offered Rate (SHIBOR). In addition, the penalty functions at Componentwise HVAR and Lag-Weighted Lasso are set according to Nicholson et al. (2017) [25].

(4)

Deleting the following sentences in “Section 3” on page 11:

• From the stock market, fuel futures and crude oil futures have a negative impact on the weighted yield of related industries, while coke futures have a positive impact on the weighted yield of related industries. The impact of industry-weighted yield on steam coal futures is negative. (in the paragraph before Table 2)
• and “, namely Lag-Weighted Lasso” (before Equation (2))

(5)

Correcting clerical errors:

• Replacing the sentences in “Section 2.5” on page 8:

First, after the introduction of the National Carbon Market, the Chinese Security Index (CSI)300 index shows a significantly positive impact on the carbon-weighted price.

• with

First, after the introduction of the National Carbon Market, the steam coal, and asphalt futures show a significantly positive impact on the carbon-weighted price.

• Replacing the words in “Section 5” on page 12:

The empirical results reveal that after the introduction of the National Carbon Market, the CSI300 index has a significantly positive impact on the carbon-weighted price.

• with

The empirical results reveal that, after the introduction of the National Carbon Market, the steam coal, and asphalt futures have a significantly positive impact on the carbon-weighted price.

• Replacing the sentences in “Section 2.3” on page 6:

The product dimension, the intermediary between financial institutions or other entities, is divided into five parts.

• with

The product dimension, the intermediary between financial institutions or other entities, is divided into three parts.

• Change Equation (3) to:

  $$\underset{v,\varphi ,\beta }{min}{\displaystyle \sum }_{t=1}^T\Vert y_t-v-{\displaystyle \sum }_{l=1}^p{\mathsf{\Phi }}^{\left(i\right)}{y}_{t-l}-{\displaystyle \sum }_{j=1}^s{\beta }^{\left(j\right)}{x}_{t-j}{\Vert }_2^2+\lambda \left(p_y\left(\mathsf{\Phi }\right)+p_x\left(\beta \right)\right),\lambda \ge 0$$

(6)

Replacing Tables with clerical errors:

Replacing the original version (Contents in the left column were in the wrong order):

Table 1. MSFE of BigVAR estimation result.

	Carbon Market Trading Volume Weighted Yield	Carbon Market Business Volume Weighted Yield
Componentwise HVAR	0.0000221	0.00000503
Lag-Weighted Lasso	0.000889679	0.000442365
Lag group	0.01001355	0.000152958

Table 1. MSFE of BigVAR estimation result.

	Carbon Market Trading Volume Weighted Yield	Carbon Market Business Volume Weighted Yield
Componentwise HVAR	0.0000221	0.00000503
Lag-Weighted Lasso	0.000889679	0.000442365
Lag group	0.01001355	0.000152958

• with

Table 1. MSFE of BigVAR estimation result.

	Carbon Market Trading Volume Weighted Yield	Carbon Market Turnover Volume Weighted Yield
Lag group	0.0000221	0.00000503
Componentwise HVAR	0.000889679	0.000442365
Lag-Weighted Lasso	0.01001355	0.000152958

Table 1. MSFE of BigVAR estimation result.

	Carbon Market Trading Volume Weighted Yield	Carbon Market Turnover Volume Weighted Yield
Lag group	0.0000221	0.00000503
Componentwise HVAR	0.000889679	0.000442365
Lag-Weighted Lasso	0.01001355	0.000152958

• Changing “Strong” influence into “General” influence
• Changing Carbon Market “trading” volume Weighted yield Carbon Market “turnover” volume Weighted yield

Replacing the original version (Changing “Strong” to “General”; changing “trading” to “turnover”):

Table 2. Summary of variable results affecting the Carbon Market.

Variables Affecting the Price of Carbon Emission Rights
Lag Group	Strong Influence	Strong Influence	Lag Group	Strong Influence	Strong Influence
Carbon Market trading volume Weighted yield	Steam coal continuous (+) Asphalt in the recent month (+) Coke in the recent month (-)	corporate debt index(+) Crude oil in the recent month (+) Fuel in the recent month (+)	Carbon Market trading volume Weighted yield	Steam coal continuous * (+) Crude oil in the recent month (+) *
National carbon market yield	Steam coal continuous(-) National debt index−) Asphalt in the recent month (+) Coke in the recent month (-)	CSI300(+) corporate debt index(+) Crude oil in the recent month (+) Fuel in the recent month (+) USD to RMB (CFETS) (+)
variables affected by the carbon emission market
Carbon Market trading volume Weighted yield	corporate debt index(-) USD to RMB (CFETS)(+) SHIBOR Overnight (+)	National debt index(+) Asphalt in the recent month (+) Fuel in the recent month (+)	Carbon Market trading volume Weighted yield	Asphalt in the recent month (+) Fuel in the recent month (+) USD to RMB (CFETS) (+)	SHIBOR Overnight (+)
National carbon market yield	corporate debt index(-) National debt index(-) Asphalt in the recent month (+) Coke in the recent month (-)	Industry weighted yield (+) CSI300(+) Crude oil in the recent month (+) Fuel in the recent month (+)

Note: (+) and (-) represent the positive and negative influence, respectively. * indicates the consistent influence of the two models.

Table 2. Summary of variable results affecting the Carbon Market.

Variables Affecting the Price of Carbon Emission Rights
Lag Group	Strong Influence	Strong Influence	Lag Group	Strong Influence	Strong Influence
Carbon Market trading volume Weighted yield	Steam coal continuous (+) Asphalt in the recent month (+) Coke in the recent month (-)	corporate debt index(+) Crude oil in the recent month (+) Fuel in the recent month (+)	Carbon Market trading volume Weighted yield	Steam coal continuous * (+) Crude oil in the recent month (+) *
National carbon market yield	Steam coal continuous(-) National debt index−) Asphalt in the recent month (+) Coke in the recent month (-)	CSI300(+) corporate debt index(+) Crude oil in the recent month (+) Fuel in the recent month (+) USD to RMB (CFETS) (+)
variables affected by the carbon emission market
Carbon Market trading volume Weighted yield	corporate debt index(-) USD to RMB (CFETS)(+) SHIBOR Overnight (+)	National debt index(+) Asphalt in the recent month (+) Fuel in the recent month (+)	Carbon Market trading volume Weighted yield	Asphalt in the recent month (+) Fuel in the recent month (+) USD to RMB (CFETS) (+)	SHIBOR Overnight (+)
National carbon market yield	corporate debt index(-) National debt index(-) Asphalt in the recent month (+) Coke in the recent month (-)	Industry weighted yield (+) CSI300(+) Crude oil in the recent month (+) Fuel in the recent month (+)

Note: (+) and (-) represent the positive and negative influence, respectively. * indicates the consistent influence of the two models.

• with:

Table 2. Summary of variable results affecting the Carbon Market.

Variables Affecting the Price of Carbon Emission Rights
Lag Group	Strong Influence	General Influence	Lag Group	Strong Influence	General Influence
Carbon Market trading volume Weighted yield	Steam coal continuous (+) Asphalt in the recent month (+) Coke in the recent month (-)	corporate debt index(+) Crude oil in the recent month (+) Fuel in the recent month (+)	Carbon Market turnover volume Weighted yield	Steam coal continuous * (+) Crude oil in the recent month (+) *
National carbon market yield	Steam coal continuous(-) National debt index(-) Asphalt in the recent month (+) Coke in the recent month (-)	CSI300(+) corporate debt index(+) Crude oil in the recent month (+) Fuel in the recent month (+) USD to RMB (CFETS) (+)
variables affected by the carbon emission market
Carbon Market trading volume Weighted yield	corporate debt index(-) USD to RMB (CFETS)(+) SHIBOR Overnight (+)	National debt index(+) Asphalt in the recent month (+) Fuel in the recent month (+)	Carbon Market turnover volume Weighted yield	Asphalt in the recent month (+) Fuel in the recent month (+) USD to RMB (CFETS) (+)	SHIBOR Overnight (+)
National carbon market yield	corporate debt index(-) National debt index(-) Asphalt in the recent month (+) Coke in the recent month (-)	Industry weighted yield (+) CSI300(+) Crude oil in the recent month (+) Fuel in the recent month (+)

Note: (+) and (-) represent the positive and negative influence, respectively. * indicates the consistent influence of the two models.

Table 2. Summary of variable results affecting the Carbon Market.

Variables Affecting the Price of Carbon Emission Rights
Lag Group	Strong Influence	General Influence	Lag Group	Strong Influence	General Influence
Carbon Market trading volume Weighted yield	Steam coal continuous (+) Asphalt in the recent month (+) Coke in the recent month (-)	corporate debt index(+) Crude oil in the recent month (+) Fuel in the recent month (+)	Carbon Market turnover volume Weighted yield	Steam coal continuous * (+) Crude oil in the recent month (+) *
National carbon market yield	Steam coal continuous(-) National debt index(-) Asphalt in the recent month (+) Coke in the recent month (-)	CSI300(+) corporate debt index(+) Crude oil in the recent month (+) Fuel in the recent month (+) USD to RMB (CFETS) (+)
variables affected by the carbon emission market
Carbon Market trading volume Weighted yield	corporate debt index(-) USD to RMB (CFETS)(+) SHIBOR Overnight (+)	National debt index(+) Asphalt in the recent month (+) Fuel in the recent month (+)	Carbon Market turnover volume Weighted yield	Asphalt in the recent month (+) Fuel in the recent month (+) USD to RMB (CFETS) (+)	SHIBOR Overnight (+)
National carbon market yield	corporate debt index(-) National debt index(-) Asphalt in the recent month (+) Coke in the recent month (-)	Industry weighted yield (+) CSI300(+) Crude oil in the recent month (+) Fuel in the recent month (+)

Note: (+) and (-) represent the positive and negative influence, respectively. * indicates the consistent influence of the two models.

(7)

The authors wish to add a reference citation in Section 2.3 (page 5)

Replacing the original version:

The product dimension explains what the Carbon Market uses. The policy dimension is used to explain how to achieve a complete framework of the Carbon Market.

• with

The product dimension explains what the Carbon Market uses. The policy dimension is used to explain how to achieve a complete framework of the Carbon Market [18].

(8)

Adding a reference in the citation list:

18. Mu, Y.F. Research on the Construction of China’s Carbon Financial System Based on a Three-Dimensional Model; Tianjin University of Finance and Economics: Tianjin, China, 2011.

• Replacing the original reference 24:

Li, Y.; Yang, X.; Ran, Q.;Wu, H.; Irfan, M.; Ahmad, M. Energy structure, digital economy, and carbon emissions: Evidence from China. Environ. Sci. Pollut. Res. 2021, 28, 64606–64629.

• with

Nicholson, W.; Matteson, D.; Bien, J. Bigvar: Tools for modeling sparse high-dimensional multivariate time series. arXiv 2017; arXiv:1702.07094.

The authors and the Editorial Office would like to apologize for any inconvenience caused to the readers, and state that the scientific conclusions are unaffected. The original article has been updated.