# Modelling Dependency Structures of Carbon Trading Markets between China and European Union: From Carbon Pilot to COVID-19 Pandemic

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## Abstract

**:**

## 1. Introduction

## 2. Methods

#### 2.1. GARCH Model

#### 2.2. Copula Model

#### 2.2.1. Basic Copula Theory

#### 2.2.2. Copula Families

#### 2.2.3. Canonical Vine (C-Vine) Copulas

#### 2.2.4. Non-Linear Correlation and Tail Correlation Metrics

## 3. Empirical Models and Data

#### 3.1. Data Description

#### 3.2. Statistical Characteristics of the Carbon Price Return Series

#### 3.3. Estimation Results of the Marginal Distribution

#### 3.4. Estimation Results of C-Vine-Copula

#### 3.4.1. Analysis of the Dependency between the Carbon Markets before and after the Launch of National ETS

#### 3.4.2. Analysis of Dependencies between Carbon Markets before and after COVID-19

## 4. Conclusions and Discussion

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A

Paris | Copula | Parameter 1 (SE) | Parameter 2 (SE) | Tau | Tail Dep | |
---|---|---|---|---|---|---|

Before the ETS | ||||||

Tree 1 | EUA-HB | t | 0.01 (0.07) | 5.46 *** (1.99) | 0.00 | 0.04 |

EUA-SH | t | 0.03 (0.06) | 5.09 *** (1.60) | 0.02 | 0.05 | |

EUA-SZ | t | −0.13 ** (0.06) | 11.51 (9.02) | −0.08 | 0.00 | |

EUA-BJ | N | 0.12 ** (0.06) | - | 0.07 | - | |

EUA-GD | t | −0.17 *** (0.06) | 9.13 (5.81) | −0.11 | 0.00 | |

Tree 2 | GD-HB|EUA | t | −0.04 (0.06) | 6.00 *** (2.20) | −0.02 | 0.03 |

GD-SH|EUA | N | 0.08 (0.05) | - | 0.05 | - | |

GD-SZ|EUA | C | 0.16 ** (0.07) | - | 0.07 | 0.01 ^{L} | |

GD-BJ|EUA | C | 0.18 ** (0.07) | - | 0.08 | 0.02 ^{L} | |

Tree 3 | BJ-HB|GD, EUA | J | 1.07 *** (0.05) | - | 0.04 | 0.09 ^{U} |

BJ-SH|GD, EUA | BB7 | 1.00 *** (0.06) | 0.11 * (0.06) | 0.05 | 0.00 | |

BJ-SZ|GD, EUA | N | −0.07 (0.06) | - | −0.04 | - | |

Tree 4 | SZ-HB|BJ, GD, EUA | C | 0.13 ** (0.06) | - | 0.06 | 0.00 ^{L} |

SZ-SH|BJ, GD, EUA | F | 0.24 (0.35) | - | 0.03 | - | |

Tree 5 | SH-HB|SZ, BJ, GD, EUA | J | 1.06 *** (0.04) | - | 0.04 | 0.08 ^{U} |

After the ETS | ||||||

Tree 1 | EUA-HB | t | −0.04 (0.06) | 7.11 *** (2,75) | −0.02 | 0.02 |

EUA-SH | t | −0.07 (0.06) | 6.41 *** (2.32) | −0.04 | 0.02 | |

EUA-SZ | t | −0.02 (0.06) | 7.45 ** (3.36) | −0.02 | 0.02 | |

EUA-BJ | F | −0.29 (0.43) | - | −0.03 | - | |

EUA-GD | N | 0.04 (0.06) | - | 0.02 | - | |

Tree 2 | BJ-SZ|EUA | F | 0.07 (0.51) | - | 0.01 | - |

BJ-GD|EUA | t | −0.09 (0.15) | 5.11 ** (2.56) | −0.05 | 0.04 | |

BJ-SH|EUA | C | 0.18 ** (0.07) | - | 0.08 | 0.02 ^{L} | |

BJ-HB|EUA | N | 0.05 (0.09) | - | 0.03 | - | |

Tree 3 | HB-SZ|BJ, EUA | F | −0.40 (0.08) | - | −0.04 | - |

HB-GD|BJ, EUA | N | −0.05 (0.07) | - | −0.03 | - | |

HB-SH|BJ, EUA | F | −0.78 * (0.42) | - | −0.09 | - | |

Tree 4 | SH-SZ|HB, BJ, EUA | N | −0.03 (0.06) | - | −0.02 | - |

SH-GD|HB, BJ, EUA | BB7 | 1.18 *** (0.12) | 0.02 (0.05) | 0.10 | 0.20 ^{U} | |

Tree 5 | GD-SZ|SH, HB, BJ, EUA | C | 0.06 (0.05) | - | 0.03 | 0.00 ^{L} |

Paris | Copula | Parameter 1 (SD) | Parameter 2 (SD) | Tau | Tail Dep | |
---|---|---|---|---|---|---|

Before COVID-19 | ||||||

Tree 1 | EUA-SZ | C | 0.04 (0.07) | - | 0.02 | 0.00 ^{L} |

EUA-GD | C | 0.07 (0.08) | - | 0.04 | 0.00 ^{L} | |

EUA-SH | t | 0.05 (0.09) | 4.00 *** (1.27) | 0.03 | 0.09 | |

EUA-HB | t | −0.09 (0.08) | 4.54 *** (1.68) | −0.05 | 0.05 | |

EUA-BJ | G | 1.01 *** (0.06) | - | 0.01 | 0.01 ^{U} | |

Tree 2 | BJ-SZ|EUA | F | −0.23 (0.66) | - | −0.03 | - |

BJ-GD|EUA | t | 0.05 (0.02) | 4.51 * (2.39) | 0.03 | 0.07 | |

BJ-SH|EUA | C | 0.25 ** (0.01) | - | 0.11 | 0.06 ^{L} | |

BJ-HB|EUA | F | 0.64 (0.62) | - | 0.07 | - | |

Tree 3 | HB-SZ|BJ, EUA | J | 1.03 *** (0.06) | - | 0.02 | 0.04 ^{U} |

HB-GD|BJ, EUA | C | 0.00 (0.08) | - | 0.00 | - | |

HB-SH|BJ, EUA | N | −0.12 (0.08) | - | −0.08 | - | |

Tree 4 | SH-SZ|HB, BJ, EUA | N | −0.01 (0.08) | - | −0.01 | - |

SH-GD|HB, BJ, EUA | J | 1.25 *** (0.13) | - | 0.12 | 0.26 ^{U} | |

Tree 5 | GD-SZ|SH, HB, BJ, EUA | C | 0.11 (0.07) | - | 0.05 | 0.00 ^{L} |

After COVID-19 | ||||||

Tree 1 | EUA-SZ | t | −0.06 (0.10) | 5.46 * (3.06) | −0.04 | 0.03 |

EUA-GD | C | 0.00 (0.10) | - | 0.00 | - | |

EUA-SH | t | −0.20 * (0.10) | 10.43 (9.42) | −0.13 | 0.00 | |

EUA-HB | t | 0.02 (0.11) | - | 0.01 | 0.01 | |

EUA-BJ | t | −0.09 (0.09) | - | −0.06 | 0.00 | |

Tree 2 | SH-GD|EUA | t | −0.09 (0.14) | - | −0.06 | 0.00 |

SH-SZ|EUA | J | 1.26 *** (0.16) | - | 0.13 | 0.27 | |

SH-BJ|EUA | F | 0.81 (0.66) | - | 0.09 | - | |

SH-HB|EUA | F | −1.18 (0.75) | - | −0.13 | - | |

Tree 3 | HB-GD|SH, EUA | G | 1.06 *** (0.10) | - | 0.06 | 0.08 ^{U} |

HB-SZ|SH, EUA | F | −1.27 (0.61) | - | −0.14 | - | |

HB-BJ|SH, EUA | F | −0.21 (0.63) | - | −0.02 | - | |

Tree 4 | BJ-GD|HB, SH, EUA | F | −0.66 (0.64) | - | −0.07 | - |

BJ-SZ|HB, SH, EUA | t | −0.01 (0.10) | - | −0.01 | 0.00 ^{U} | |

Tree 5 | SZ-GD|BJ, HB, SH, EUA | F | 0.63 (0.63) | - | 0.07 | - |

## References

- Rajalingam, M.; Srivastava, A. Rational hybrid analytical model for steel pipe rack quantification in oil & gas industries. Civ. Eng. J.
**2020**, 6, 649–658. [Google Scholar] [CrossRef][Green Version] - Zeng, S.H.; Jia, J.M.; Su, B.; Jiang, C.X.; Zeng, G.W. The volatility spillover effect of the European Union (EU) carbon financial market. J. Clean. Prod.
**2021**, 282, 124394. [Google Scholar] [CrossRef] - Lin, B.; Chen, Y. Dynamic linkages and spillover effects between CET market, coal market and stock market of new energy companies: A case of Beijing CET market in China. Energy
**2019**, 172, 1198–1210. [Google Scholar] [CrossRef] - Stoerk, T.; Dudek, D.J.; Yang, J. China’s national carbon emissions trading scheme: Lessons from the pilot emission trading schemes, academic literature, and known policy details. Clim. Policy
**2019**, 19, 472–486. [Google Scholar] [CrossRef] - Wen, F.; Wu, N.; Gong, X. China’s carbon emissions trading and stock returns. Energy Econ.
**2020**, 86, 104627. [Google Scholar] [CrossRef] - Sun, L.M.; Xiang, M.Q.; Shen, Q. A comparative study on the volatility of EU and China’s carbon emission permits trading markets. Phys. A
**2020**, 560, 125037. [Google Scholar] [CrossRef] - Benkraiem, R.; Garfatta, R.; Lakhal, F.; Zorgati, I. Financial contagion intensity during the COVID-19 outbreak: A copula approach. Int. Rev. Financ. Anal.
**2022**, 81, 102136. [Google Scholar] [CrossRef] - Liu, J.X.; Cheng, Y.N.; Li, X.Q.; Sriboonchitta, S. The role of risk forecast and risk tolerance in portfolio management: A case study of the Chinese financial sector. Axioms
**2022**, 11, 134. [Google Scholar] [CrossRef] - Rupani, P.F.; Nilashi, M.; Abumalloh, R.A.; Asadi, S.; Samad, S.; Wang, S. Coronavirus pandemic (COVID-19) and its natural environmental impacts. Int. J. Environ. Sci. Technol.
**2020**, 17, 4655–4666. [Google Scholar] [CrossRef] - Corbet, S.; Hou, Y.; Hu, Y.; Lucey, B.; Oxley, L. Aye Corona! The contagion effects of being named Corona during the COVID-19 pandemic. Financ. Res. Lett.
**2021**, 38, 101591. [Google Scholar] [CrossRef] - Zhang, Y.; Sun, Y. The dynamic volatility spillover between European carbon trading market and fossil energy market. J. Clean. Prod.
**2016**, 112, 2654–2663. [Google Scholar] [CrossRef] - Dhamija, A.K.; Yadav, S.S.; Jain, P.K. Volatility spillover of energy markets into EUA markets under EU ETS: A multi-phase study. Environ. Econ. Policy Stud.
**2017**, 20, 561–591. [Google Scholar] [CrossRef] - Wu, Q.; Wang, M.; Tian, L. The market-linkage of the volatility spillover between traditional energy price and carbon price on the realization of carbon value of emission reduction behavior. J. Clean. Prod.
**2020**, 245, 118682. [Google Scholar] [CrossRef] - Hanif, W.; Hernandez, J.A.; Mensi, W.; Kang, S.H.; Uddin, G.S.; Yoon, S.M. Nonlinear dependence and connectedness between clean/renewable energy sector equity and European emission allowance prices. Energy Econ.
**2021**, 101, 105409. [Google Scholar] [CrossRef] - Chang, K.; Ye, Z.F.; Wang, W.H. Volatility spillover effect and dynamic correlation between regional emissions allowances and fossil energy markets: New evidence from China’s emissions trading scheme pilots. Energy
**2019**, 185, 1314–1324. [Google Scholar] [CrossRef] - Reboredo, J.C. Volatility spillovers between the oil market and the European Union carbon emission market. Econ. Model
**2014**, 36, 229–234. [Google Scholar] [CrossRef] - Zhu, B.Z.; Huang, L.Q.; Yuan, L.L.; Ye, S.X.; Wang, P. Exploring the risk spillover effects between carbon market and electricity market: A bidimensional empirical mode decomposition based conditional value at risk approach. Int. Rev. Econ. Financ.
**2020**, 67, 163–175. [Google Scholar] [CrossRef] - Xu, L.; Wu, C.Y.; Qin, Q.D.; Lin, X.Y. Spillover effects and nonlinear correlations between carbon emissions and stock markets: An empirical analysis of China’s carbon-intensive industries. Energy Econ.
**2022**, 111, 106071. [Google Scholar] [CrossRef] - Oestreich, A.M.; Tsiakas, I. Carbon emissions and stock returns: Evidence from the EU emissions trading scheme. J. Bank. Financ.
**2015**, 58, 294–308. [Google Scholar] [CrossRef] - Hu, G.H.; Wu, H.Y.; Qiu, J.X. Dependence structure of carbon emission markets: Regular Vine approach. Chin. J. Popul. Resour.
**2015**, 25, 44–52. [Google Scholar] - Arouri, M.E.H.; Jawadi, F.; Nguyen, D.K. Nonlinearities in carbon spot-futures price relationships during Phase II of the EU ETS. Econ. Model.
**2012**, 29, 884–892. [Google Scholar] [CrossRef] - Zhao, L.L.; Wen, F.H.; Wang, X. Interaction among China carbon emission trading markets: Nonlinear Granger causality and time-varying effect. Energy Econ.
**2020**, 91, 104901. [Google Scholar] [CrossRef] - Zhu, B.Z.; Zhou, X.X.; Liu, X.F.; Wang, H.F.; He, K.J.; Wang, P. Exploring the risk spillover effects among China’s pilot carbon markets: A regular vine copula-CoES approach. J. Clean. Prod.
**2020**, 242, 118455. [Google Scholar] [CrossRef] - Mai, T.K.; Foley, A.M.; McAleer, M.; Chang, C.L. Impact of COVID-19 on returns-volatility spillovers in national and regional carbon markets in China. Renew. Sustain. Energy Rev.
**2022**, 169, 112861. [Google Scholar] [CrossRef] - Fang, S.; Cao, G.X. Modelling extreme risks for carbon emission allowances—Evidence from European and Chinese carbon markets. J. Clean. Prod.
**2021**, 316, 128023. [Google Scholar] [CrossRef] - Du, J.Z. Examining the Inter-relationship between RMB Markets. Procedia Comput. Sci.
**2018**, 139, 313–320. [Google Scholar] [CrossRef] - Wu, C.C.; Chung, H.; Chang, Y.H. The economic value of co-movement between oil price and exchange rate using copula-based GARCH models. Energy Econ.
**2012**, 34, 270–282. [Google Scholar] [CrossRef] - Benlagha, N. Dependence structure between nominal and index-linked bond returns: A bivariate copula and DCC-GARCH approach. Appl. Econ.
**2014**, 46, 3849–3860. [Google Scholar] [CrossRef] - Min, A.; Czado, C. Bayesian inference for multivariate copulas using pair-copula constructions. J. Financ. Econom.
**2010**, 8, 511–546. [Google Scholar] [CrossRef] - Embrechts, P.; McNeil, A.; Straumann, D. Correlation and Dependence in Risk Management: Properties and Pitfalls. Risk Manag. Value Risk Beyond
**2002**, 1, 176–223. [Google Scholar] - So, M.K.; Yeung, C.Y. Vine-copula GARCH model with dynamic conditional dependence. Comput. Stat. Data Anal.
**2014**, 76, 655–671. [Google Scholar] [CrossRef] - Bedford, T.; Cooke, R.M. Probability Density Decomposition for Conditionally Dependent Random Variables Modeled by Vines. Ann. Math. Artif. Intel.
**2001**, 32, 245–268. [Google Scholar] [CrossRef] - Bedford, T.; Cooke, R.M. Vines: A New Graphical Model for Dependent Random Variables. Ann. Stat.
**2002**, 30, 1031–1068. [Google Scholar] [CrossRef] - Brechmann, E.C.; Czado, C. Risk management with high-dimensional vine copulas: An analysis of the Euro Stoxx 50. Statist. Risk. Model
**2013**, 30, 307–342. [Google Scholar] [CrossRef] - Song, Q.; Liu, J.X.; Sriboonchitta, S. Risk Measurement of Stock Markets in BRICS, G7, and G20: Vine Copulas versus Factor Copulas. Mathematics
**2019**, 7, 274. [Google Scholar] [CrossRef][Green Version] - Zhang, X.M.; Zhang, T.; Lee, C.C. The path of financial risk spillover in the stock market based on the R-vine-Copula model. Phys. A
**2022**, 600, 127470. [Google Scholar] [CrossRef] - Jiang, C.X.; Li, Y.Q.; Xu, Q.F.; Liu, Y.Z. Measuring risk spillovers from multiple developed stock markets to China: A vine-copula-GARCH-MIDAS model. Int. Rev. Econ. Financ.
**2021**, 75, 386–398. [Google Scholar] [CrossRef] - Joe, H. Asymptotic efficiency of the two-stage estimation method for copula-based models. J. Multivariate. Anal.
**2005**, 94, 401–419. [Google Scholar] [CrossRef][Green Version] - Bollerslev, T. Generalized autoregressive conditional heteroskedasticity. J. Econom.
**1986**, 31, 307–327. [Google Scholar] [CrossRef][Green Version] - Bentes, S.R. On the stylized facts of precious metals’ volatility: A comparative analysis of pre-and during COVID-19 crisis. Phys. A Stat. Mech. Appl.
**2022**, 600, 127528. [Google Scholar] [CrossRef] - Huang, J.J.; Lee, K.J.; Liang, H.M.; Lin, W.F. Estimating value at risk of portfolio by conditional copula-GARCH method. Insur. Math. Econ.
**2009**, 45, 315–324. [Google Scholar] [CrossRef] - Sklar, A. Fonctions de Répartition à n Dimensions et Leurs Marges. Publ. Inst. Statist. Univ. Paris.
**1959**, 8, 229–231. [Google Scholar] - Embrechts, P.; Lindskog, F.; McNeil, A. Modelling dependence with copulas and applications to risk management. In Handbook of Heavy Tailed Distributions in Finance; Rachev, S., Ed., Elsevier: Amsterdam, The Netherlands, 2003; pp. 25–26. [Google Scholar] [CrossRef]
- Patton, A.J. Modelling asymmetric exchange rate dependence. Int. Econ. Rev.
**2006**, 47, 527–556. [Google Scholar] [CrossRef][Green Version] - Frank, M.J. On the simultaneous associativity of F(x,y) and x+y−F(x,y). Aequ. Math.
**1979**, 19, 194–226. [Google Scholar] [CrossRef] - Joe, H. Parametric families of multivariate distributions with given margins. J. Multivar. Anal.
**1993**, 46, 262–282. [Google Scholar] [CrossRef][Green Version] - Gumbel, E.J. Bivariate exponential distributions. J. Am. Stat. Assoc.
**1960**, 55, 698–707. [Google Scholar] [CrossRef] - Clayton, D.G. A model for association in bivariate life tables and its application in epidemiological studies of familial tendency in chronic disease incidence. Biometrika
**1978**, 65, 141–152. [Google Scholar] [CrossRef] - Ly, L.; Sriboonchitta, S.; Tang, J.C.; Wong, W.K. Exploring dependence structures among European electricity markets: Static and dynamic copula-GARCH and dynamic state-space approaches. Energy Rep.
**2022**, 8, 3827–3846. [Google Scholar] [CrossRef] - Sriboonchitta, S.; Nguyen, H.T.; Wiboonpongse, A.; Liu, J.X. Modeling volatility and dependency of agricultural price and production indices of Thailand: Static versus time-varying copulas. Int. J. Approx. Reason.
**2013**, 54, 793–808. [Google Scholar] [CrossRef] - Viviana, F. Copula-based measures of dependence structure in assets returns. Phys. A
**2008**, 387, 3615–3628. [Google Scholar] [CrossRef] - Akaike, H. Information theory and an extension of the maximum likelihood principle. In Selected Papers of Hirotugu Akaike; Parzen, E., Tanabe, K., Kitagawa, G., Eds.; Springer: New York, NY, USA, 1998; pp. 199–213. [Google Scholar]
- Brechmann, E.C. Truncated and simplified regular vines and their applications. Ph.D. Thesis, Technische Universitaet Muenchen, Munich, Germany, 2010. [Google Scholar]
- Emmanouil, K.N.; Nikos, N. Extreme Value Theory and Mixed Canonical Vine Copulas on Modelling Energy Price Risks; Working Paper; NTNU: Trondheim, Norway, 2012. [Google Scholar]
- Tachibana, M. Relationship between stock and currency markets conditional on the US stock returns: A vine copula approach. J. Multinatl. Financ. Manag.
**2018**, 46, 75–106. [Google Scholar] [CrossRef][Green Version] - Wei, Z.; Kim, S.Y.; Kim, D.Y. Multivariate Skew Normal Copula for non-exchangeable dependence. Procedia Comput. Sci.
**2016**, 91, 141–150. [Google Scholar] [CrossRef] - Schweizer, B.; Wolff, E. On nonparametric measures of dependence for random variables. Ann. Stat.
**1981**, 9, 879–885. [Google Scholar] [CrossRef] - Qiu, Q.; Guo, S.Q. Analysis of regional trading market risks in carbon finance. Resour. Dev. Market.
**2017**, 2, 188–193. [Google Scholar]

**Figure 2.**Daily closing price of carbon trading market, April 2014 to June 2021. Notes: The dividing point of the first vertical line is 16 December 2017, the official launch date of the national ETS in China; The dividing point of the second vertical line is 1 January 2020, the date of the global COVID-19 outbreak; The same below.

Mean | Med | Max | Min | SD | Skew | Kurt | ADF | LB-Q | ARCH-LM | J-B | |
---|---|---|---|---|---|---|---|---|---|---|---|

Before the ETS (2 April 2014 to 16 December 2017) | |||||||||||

EUA | 0.16 | 0.00 | 31.61 | −33.44 | 5.06 | −0.44 | 13.76 | −6.44 ** | 11.71 * | 8.83 | 2304.30 *** |

SZ | −0.27 | −0.24 | 44.60 | −40.48 | 13.64 | 0.03 | 1.12 | −8.71 ** | 54.75 *** | 22.94 * | 15.7630 *** |

SH | −0.04 | 0.00 | 46.95 | −51.35 | 9.17 | −0.89 | 11.08 | −4.74 ** | 24.76 *** | 71.62 *** | 1527.30 *** |

BJ | 0.01 | 0.00 | 34.56 | −28.31 | 6.67 | −0.10 | 5.88 | −9.87 ** | 30.49 *** | 84.72 *** | 421.70 *** |

GD | −0.55 | −0.01 | 39.01 | −77.43 | 11.63 | −0.97 | 7.38 | −7.20 ** | 15.20 ** | 5.03 | 706.95 *** |

HB | −0.14 | −0.21 | 17.57 | −13.84 | 3.67 | 0.65 | 5.10 | −6.13 ** | 10.05 | 19.56 * | 336.79 *** |

After the ETS (17 December 2017 to 16 July 2021) | |||||||||||

EUA | 0.67 | 0.22 | 31.65 | −41.32 | 6.07 | −0.01 | 13.92 | −6.67 ** | 6.95 | 14.53 | 2300.80 *** |

SZ | −0.46 | −0.17 | 196.35 | −162.06 | 42.74 | 0.07 | 3.60 | −8.35 ** | 55.14 *** | 79.63 *** | 155.73 *** |

SH | 0.05 | 0.00 | 24.09 | −23.64 | 6.06 | 0.32 | 3.69 | −8.50 ** | 18.85 ** | 64.09 *** | 168.03 *** |

BJ | 0.04 | 0.35 | 62.99 | −54.39 | 12.07 | 0.05 | 5.16 | −7.65 ** | 6.26 | 39.27 *** | 318.21 *** |

GD | 0.44 | 0.32 | 265.63 | −244.13 | 30.20 | 0.47 | 37.96 | −11.94 ** | 74.06 *** | 6.00 | 17,078.00 *** |

HB | 0.26 | 0.07 | 22.68 | −22.35 | 4.27 | 0.47 | 7.72 | −6.54 ** | 16.50 ** | 71.74 *** | 718.68 *** |

Mean | Med | Max | Min | SD | Skew | Kurt | ADF | LB-Q | ARCH-LM | J-B | |
---|---|---|---|---|---|---|---|---|---|---|---|

Before COVID-19 (18 December 2017 to 31 December 2019) | |||||||||||

EUA | 0.65 | 0.21 | 31.65 | −22.10 | 5.40 | 0.87 | 9.40 | −6.04 ** | 5.59 | 7.81 | 667.34 *** |

SZ | −1.07 | −0.69 | 196.35 | −147.26 | 37.30 | 0.41 | 6.65 | −6.45 ** | 41.43 *** | 63.67 *** | 329.43 *** |

SH | 0.16 | 0.01 | 23.77 | −23.64 | 6.16 | 0.06 | 3.57 | −5.82 ** | 13.45 ** | 22.32 ** | 94.52 *** |

BJ | 0.15 | 0.35 | 62.99 | −54.39 | 11.13 | 0.46 | 9.60 | −7.76 ** | 12.94 ** | 14.71 | 679.97 *** |

GD | 0.45 | 0.25 | 265.63 | −244.13 | 34.95 | 0.48 | 32.75 | −11.54 ** | 43.68 *** | 3.91 | 7802.40 *** |

HB | 0.31 | 0.13 | 22.68 | −22.35 | 5.04 | 0.36 | 5.71 | −6.07 ** | 11.37 ** | 39.11 *** | 243.18 *** |

After COVID-19 (1 January 2020 to 16 July 2021) | |||||||||||

EUA | 0.70 | 0.31 | 30.87 | −41.32 | 7.01 | −0.64 | 14.51 | −4.75 ** | 9.21 * | 5.62 | 1016.10 *** |

SZ | 0.50 | 2.62 | 157.62 | −162.06 | 50.16 | −0.18 | 1.32 | −8.45 ** | 29.84 *** | 35.32 *** | 9.52 *** |

SH | −0.11 | −0.02 | 24.09 | −14.72 | 5.92 | 0.77 | 3.83 | −6.46 ** | 7.53 | 49.10 *** | 82.85 *** |

BJ | −0.14 | 0.35 | 41.36 | −44.64 | 13.44 | −0.31 | 1.31 | −5.07 ** | 5.51 | 30.35 *** | 10.67 *** |

GD | 0.41 | 0.38 | 122.95 | −118.82 | 20.99 | 0.10 | 19.06 | −10.84 ** | 36.57 *** | 0.17 | 1736.60 *** |

HB | 0.18 | 0.00 | 12.56 | −7.14 | 2.71 | 0.87 | 4.28 | −6.09 ** | 14.65 ** | 6.07 | 103.81 *** |

**Table 3.**Estimation results for the marginal models of carbon trading price (before and after the ETS).

EUA | SZ | SH | BJ | GD | HB | |
---|---|---|---|---|---|---|

Before the ETS | ||||||

$\mu $ | 0.136 (1.318) | −0.010 (−0.046) | 0.051 (0.259) | −0.031 (−0.818) | −0.576 ** (−1.987) | −0.1207 (−1.5031) |

$\phi $ | 0.839 *** (7.788) | 0.117 (1.017) | 0.208 (0.559) | 0.341 *** (4.004) | 0.866 *** (14.541) | 0.3486 * (1.7973) |

$\theta $ | −0.898 *** (−11.07) | −0.652 *** (−7.273) | −0.263 (−0.720) | −0.754 *** (−14.531) | −0.931 *** (−23.767) | −0.5373 *** (−3.1335) |

$\omega $ | 2.766 *** (1.561) | 38.327 ** (2.247) | 3.005 (0.701) | 0.726 * (1.907) | 0.624 (0.564) | 2.313 * (1.710) |

$\alpha $ | 0.294 (1.717) | 0.440 ** (2.471) | 0.223 (1.575) | 0.452 *** (5.160) | 0.000 (0.000) | 0.586 *** (3.444) |

$\beta $ | 0.705 * (6.539) | 0.415 *** (2.929) | 0.776 *** (3.270) | 0.547 *** (7.657) | 0.998 *** (258.868) | 0.4134 *** (3.103) |

$t$ | 2.679 *** (6.614) | 4.660 *** (3.184) | 2.571 *** (6.802) | 3.221 *** (10.192) | 3.008 *** (7.529) | 2.982 *** (7.644) |

Log Likelihood | −776.840 | −1094.306 | −910.867 | −788.050 | −1072.289 | −708.530 |

AIC | 5.481 | 7.701 | 6.419 | 5.560 | 7.548 | 5.004 |

After the ETS | ||||||

$\mu $ | 0.2927 (1.5831) | −0.3993 (−0.9552) | 0.0504 (0.6447) | 0.2575 (1.6373) | 0.6521 *** (3.9178) | 0.1266 (1.5472) |

$\phi $ | 0.5309 * (1.7602) | 0.1290 (1.1770) | −0.0290 (−0.1986) | −0.3787 (−0.9173) | −0.1397 (−1.2428) | 0.2444 * (1.7600) |

$\theta $ | −0.5849 ** (−2.0432) | −0.6901 *** (−7.9853) | −0.2795 ** (−1.9372) | 0.3025 (0.7052) | −0.3655 *** (−2.4946) | −0.4889 *** (−4.3270) |

$\omega $ | 0.1325 (0.3122) | 67.3125 * (1.7400) | 3.5917 *** (3.3980) | 1.1349 (1.2763) | 40.4564 ** (2.5465) | 1.4791 (1.0746) |

$\alpha $ | 0.0020 (0.1802) | 0.3641 *** (3.5845) | 0.8556 *** (5.0966) | 0.4171 *** (5.4491) | 0.8010 *** (3.7382) | 0.4970 *** (3.6056) |

$\beta $ | 0.9970 *** (319.4716) | 0.6349 *** (7.7451) | 0.1434 ** (2.1148) | 0.5819 *** (7.9922) | 0.1980* (1.4737) | 0.5020 *** (3.2861) |

$t$ | 2.3601 *** (17.4461) | 3.8608 *** (4.9929) | 2.8252 *** (13.2582) | 3.2452 *** (10.8275) | 2.4369 *** (18.6968) | 3.1149 *** (7.9993) |

Log Likelihood | −812.3930 | −1342.6590 | −779.2891 | −966.5379 | −1026.1220 | −714.4188 |

AIC | 5.8528 | 9.6404 | 5.6164 | 6.9538 | 7.3794 | 5.1530 |

**Table 4.**Estimation results for the marginal models of carbon trading price (before and after COVID-19).

EUA | SZ | SH | BJ | GD | HB | |
---|---|---|---|---|---|---|

Before COVID-19 | ||||||

$\mu $ | 0.1044 (0.2339) | −0.4071 (0.5098) | 0.1134 (0.1244) | 0.2981 ** (0.1384) | 0.5883 *** (0.1488) | 0.2532 (0.2162) |

$\phi $ | −0.8796 *** (0.0763) | 0.0310 (0.2454) | −0.0468 (0.2233) | −0.5355 ** (0.2121) | 0.0797 (0.1140) | −0.7748 *** (0.1943) |

$\theta $ | 0.9240 *** (0.0554) | −0.5766 ** (0.2310) | −0.3145 (0.2202) | 0.4605 ** (0.2249) | −0.7152 *** (0.1005) | 0.8087 *** (0.1673) |

$\omega $ | 2.2543 (1.7493) | 71.0614 * (40.2515) | 5.3587 ** (2.5041) | 1.8210 * (1.0958) | 21.6148 (16.2651) | 4.2006 (2.7023) |

$\alpha $ | 0.1069 (0.0842) | 0.4436 *** (0.1578) | 0.7522 *** (0.2234) | 0.5121 *** (0.1355) | 0.4360 *** (0.1532) | 0.573 ** (0.2486) |

$\beta $ | 0.8388 *** (0.0639) | 0.5554 *** (0.1067) | 0.2468 ** (0.1240) | 0.4869 *** (0.0933) | 0.5630 *** (0.1956) | 0.426 *** (0.1468) |

$t$ | 2.5449 *** (0.3796) | 3.2428 *** (0.5764) | 2.8666 *** (0.3272) | 2.555 *** (0.1716) | 2.4728 *** (0.2043) | 3.2133 *** (0.6917) |

Log Likelihood | −477.4436 | −778.2724 | −496.439 | −529.1808 | −645.2967 | −475.2599 |

AIC | 5.6993 | 9.2385 | 5.9228 | 6.3080 | 7.6741 | 5.6736 |

After COVID-19 | ||||||

$\mu $ | 0.4248 (0.3238) | −0.3455 (1.4400) | −0.1327 *** (0.0211) | 0.0806 (0.6318) | 0.6640 *** (0.2276) | 0.0595 (0.0723) |

$\phi $ | 0.3740 (0.4237) | 0.1234 (0.1677) | 0.9633 *** (0.0082) | −0.7511 *** (0.1701) | −0.1990 (0.1438) | 0.0700 (0.1945) |

$\theta $ | −0.4497 (0.4060) | −0.6754 *** (0.1214) | −1.0000 *** (0.0024) | 0.8390 *** (0.1287) | −0.3729 ** (0.1701) | −0.4258 *** (0.1477) |

$\omega $ | 0.1183 (2.2655) | 152.4128 (245.6283) | 1.4005 *** (0.5300) | 5.4548 (4.7713) | 29.0942 * (17.4163) | 1.1436 (0.9136) |

$\alpha $ | 0.0000 (0.0315) | 0.2898 (0.1871) | 0.9990 *** (0.2441) | 0.3982 ** (0.1556) | 0.8014 ** (0.3803) | 0.7657 ** (0.3310) |

$\beta $ | 0.9990 *** (0.0428) | 0.6598 *** (0.2154) | 0.0000 (0.0088) | 0.6008 *** (0.1358) | 0.1976 (0.1239) | 0.2333 (0.1947) |

$t$ | 2.4435 ** (1.0165) | 5.6228 *** (4.6862) | 2.8528 *** (0.2913) | 32.3070 (78.3328) | 2.3974 *** (0.2040) | 3.1404 *** (0.5656) |

Log Likelihood | 6.1231 | 10.321 | 5.0838 | 7.6978 | 6.9685 | 4.4099 |

AIC | −329.7686 | −560.6668 | −272.609 | −416.3775 | −376.2652 | −235.543 |

Paris | Copula | Parameter 1 (SE) | Parameter 2 (SE) | Tau | Tail Dep | |
---|---|---|---|---|---|---|

Before the ETS | ||||||

Tree 1 | EUA-HB | t | 0.01 (0.07) | 5.46 *** (1.99) | 0.00 | 0.04 |

EUA-SH | t | 0.03 (0.06) | 5.09 *** (1.60) | 0.02 | 0.05 | |

EUA-SZ | t | −0.13 ** (0.06) | 11.51 (9.02) | −0.08 | 0.00 | |

EUA-BJ | N | 0.12 ** (0.06) | - | 0.07 | - | |

EUA-GD | t | −0.17 *** (0.06) | 9.13 (5.81) | −0.11 | 0.00 | |

Tree 2 | GD-HB|EUA | t | −0.04 (0.06) | 6.00 *** (2.20) | −0.02 | 0.03 |

GD-SH|EUA | N | 0.08 (0.05) | - | 0.05 | - | |

GD-SZ|EUA | C | 0.16 ** (0.07) | - | 0.07 | 0.01 ^{L} | |

GD-BJ|EUA | C | 0.18 ** (0.07) | - | 0.08 | 0.02 ^{L} | |

After the ETS | ||||||

Tree 1 | EUA-HB | t | −0.04 (0.06) | 7.11 *** (2,75) | −0.02 | 0.02 |

EUA-SH | t | −0.07 (0.06) | 6.41 *** (2.32) | −0.04 | 0.02 | |

EUA-SZ | t | −0.02 (0.06) | 7.45 ** (3.36) | −0.02 | 0.02 | |

EUA-BJ | F | −0.29 (0.43) | - | −0.03 | - | |

EUA-GD | N | 0.04 (0.06) | - | 0.02 | - | |

Tree 2 | BJ-SZ|EUA | F | 0.07 (0.51) | - | 0.01 | - |

BJ-GD|EUA | t | −0.09 (0.15) | 5.11 ** (2.56) | −0.05 | 0.04 | |

BJ-SH|EUA | C | 0.18 ** (0.07) | - | 0.08 | 0.02 ^{L} | |

BJ-HB|EUA | N | 0.05 (0.09) | - | 0.03 | - |

Paris | Copula | Parameter 1 (SD) | Parameter 2 (SD) | Tau | Tail dep | |
---|---|---|---|---|---|---|

Before COVID-19 | ||||||

Tree 1 | EUA-SZ | C | 0.04 (0.07) | - | 0.02 | 0.00 ^{L} |

EUA-GD | C | 0.07 (0.08) | - | 0.04 | 0.00 ^{L} | |

EUA-SH | t | 0.05 (0.09) | 4.00 *** (1.27) | 0.03 | 0.09 | |

EUA-HB | t | −0.09 (0.08) | 4.54 *** (1.68) | −0.05 | 0.05 | |

EUA-BJ | G | 1.01 *** (0.06) | - | 0.01 | 0.01 ^{U} | |

Tree 2 | BJ-SZ|EUA | F | −0.23 (0.66) | - | −0.03 | - |

BJ-GD|EUA | t | 0.05 (0.02) | 4.51 * (2.39) | 0.03 | 0.07 | |

BJ-SH|EUA | C | 0.25 ** (0.01) | - | 0.11 | 0.06 ^{L} | |

BJ-HB|EUA | F | 0.64 (0.62) | - | 0.07 | - | |

After COVID-19 | ||||||

Tree 1 | EUA-SZ | t | −0.06 (0.10) | 5.46 * (3.06) | −0.04 | 0.03 |

EUA-GD | C | 0.00 (0.10) | - | 0.00 | - | |

EUA-SH | t | −0.20 * (0.10) | 10.43 (9.42) | −0.13 | 0.00 | |

EUA-HB | t | 0.02 (0.11) | - | 0.01 | 0.01 | |

EUA-BJ | t | −0.09 (0.09) | - | −0.06 | 0.00 | |

Tree 2 | SH-GD|EUA | t | −0.09 (0.14) | - | −0.06 | 0.00 |

SH-SZ|EUA | J | 1.26 *** (0.16) | - | 0.13 | 0.27 | |

SH-BJ|EUA | F | 0.81 (0.66) | - | 0.09 | - | |

SH-HB|EUA | F | −1.18 (0.75) | - | −0.13 | - |

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## Share and Cite

**MDPI and ACS Style**

Zhang, M.; Liu, H.; Liu, J.; Chen, C.; Li, Z.; Wang, B.; Sriboonchitta, S.
Modelling Dependency Structures of Carbon Trading Markets between China and European Union: From Carbon Pilot to COVID-19 Pandemic. *Axioms* **2022**, *11*, 695.
https://doi.org/10.3390/axioms11120695

**AMA Style**

Zhang M, Liu H, Liu J, Chen C, Li Z, Wang B, Sriboonchitta S.
Modelling Dependency Structures of Carbon Trading Markets between China and European Union: From Carbon Pilot to COVID-19 Pandemic. *Axioms*. 2022; 11(12):695.
https://doi.org/10.3390/axioms11120695

**Chicago/Turabian Style**

Zhang, Mingzhi, Hongyu Liu, Jianxu Liu, Chao Chen, Zhaocheng Li, Bowen Wang, and Songsak Sriboonchitta.
2022. "Modelling Dependency Structures of Carbon Trading Markets between China and European Union: From Carbon Pilot to COVID-19 Pandemic" *Axioms* 11, no. 12: 695.
https://doi.org/10.3390/axioms11120695