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Multifractal detrended cross-correlation analysis of carbon emission allowance and stock returns


  • Fang, Sheng
  • Lu, Xinsheng
  • Li, Jianfeng
  • Qu, Ling


The nonlinear relationship between carbon emission allowance and stock markets has attracted special attention from economists around the world. This paper uses the technique of multifractal detrended cross-correlation analysis (MF-DCCA) to investigate the cross-correlations between carbon emission allowance and stock series as well as their dynamics for European and Chinese markets, respectively. The results show that the cross-correlations between carbon and stock series are significantly multifractal in European and Chinese markets. The cross-correlations of small fluctuations are persistent while those of large fluctuations are anti-persistent. Moreover, the degree and width of multifractality is found to be stronger in China than in Europe. We confirm that the multifractality of cross-correlations could be attributed to both the persistence of fluctuations of carbon emission allowance and stock markets and fat-tail distributions of the time series. By employing rolling estimate of MF-DCCA, we find that the scaling exponent varies over time and across fluctuations in European and Chinese markets. In particular, the Hurst exponent fluctuates around 0.5 in recent years.

Suggested Citation

  • Fang, Sheng & Lu, Xinsheng & Li, Jianfeng & Qu, Ling, 2018. "Multifractal detrended cross-correlation analysis of carbon emission allowance and stock returns," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 509(C), pages 551-566.
  • Handle: RePEc:eee:phsmap:v:509:y:2018:i:c:p:551-566
    DOI: 10.1016/j.physa.2018.05.136

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    References listed on IDEAS

    1. Jiang, Zhi-Qiang & Zhou, Wei-Xing, 2008. "Multifractal analysis of Chinese stock volatilities based on the partition function approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(19), pages 4881-4888.
    2. Bertrand, Vincent, 2014. "Carbon and energy prices under uncertainty: A theoretical analysis of fuel switching with heterogenous power plants," Resource and Energy Economics, Elsevier, vol. 38(C), pages 198-220.
    3. Ralf Martin & Mirabelle Muûls & Ulrich J. Wagner, 2016. "The Impact of the European Union Emissions Trading Scheme on Regulated Firms: What Is the Evidence after Ten Years?," Review of Environmental Economics and Policy, Association of Environmental and Resource Economists, vol. 10(1), pages 129-148.
    4. Zhang, Yue-Jun & Da, Ya-Bin, 2015. "The decomposition of energy-related carbon emission and its decoupling with economic growth in China," Renewable and Sustainable Energy Reviews, Elsevier, vol. 41(C), pages 1255-1266.
    5. Chevallier, Julien, 2009. "Carbon futures and macroeconomic risk factors: A view from the EU ETS," Energy Economics, Elsevier, vol. 31(4), pages 614-625, July.
    6. Hintermann, Beat, 2010. "Allowance price drivers in the first phase of the EU ETS," Journal of Environmental Economics and Management, Elsevier, vol. 59(1), pages 43-56, January.
    7. Lutz, Benjamin Johannes & Pigorsch, Uta & Rotfuß, Waldemar, 2013. "Nonlinearity in cap-and-trade systems: The EUA price and its fundamentals," Energy Economics, Elsevier, vol. 40(C), pages 222-232.
    8. repec:dau:papers:123456789/4222 is not listed on IDEAS
    9. Demailly, Damien & Quirion, Philippe, 2008. "European Emission Trading Scheme and competitiveness: A case study on the iron and steel industry," Energy Economics, Elsevier, vol. 30(4), pages 2009-2027, July.
    10. Zhang, Yue-Jun & Wei, Yi-Ming, 2010. "An overview of current research on EU ETS: Evidence from its operating mechanism and economic effect," Applied Energy, Elsevier, vol. 87(6), pages 1804-1814, June.
    11. Creti, Anna & Jouvet, Pierre-André & Mignon, Valérie, 2012. "Carbon price drivers: Phase I versus Phase II equilibrium?," Energy Economics, Elsevier, vol. 34(1), pages 327-334.
    12. Seifert, Jan & Uhrig-Homburg, Marliese & Wagner, Michael, 2008. "Dynamic behavior of CO2 spot prices," Journal of Environmental Economics and Management, Elsevier, vol. 56(2), pages 180-194, September.
    13. Wang, Yudong & Wei, Yu & Wu, Chongfeng, 2011. "Analysis of the efficiency and multifractality of gold markets based on multifractal detrended fluctuation analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(5), pages 817-827.
    14. Zheng, Zeyu & Xiao, Rui & Shi, Haibo & Li, Guihong & Zhou, Xiaofeng, 2015. "Statistical regularities of Carbon emission trading market: Evidence from European Union allowances," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 426(C), pages 9-15.
    15. Jia, Jun-Jun & Xu, Jin-Hua & Fan, Ying, 2016. "The impact of verified emissions announcements on the European Union emissions trading scheme: A bilaterally modified dummy variable modelling analysis," Applied Energy, Elsevier, vol. 173(C), pages 567-577.
    16. Oberndorfer, Ulrich, 2009. "EU Emission Allowances and the stock market: Evidence from the electricity industry," Ecological Economics, Elsevier, vol. 68(4), pages 1116-1126, February.
    17. Oestreich, A. Marcel & Tsiakas, Ilias, 2015. "Carbon emissions and stock returns: Evidence from the EU Emissions Trading Scheme," Journal of Banking & Finance, Elsevier, vol. 58(C), pages 294-308.
    18. Arouri, Mohamed El Hédi & Jawadi, Fredj & Nguyen, Duc Khuong, 2012. "Nonlinearities in carbon spot-futures price relationships during Phase II of the EU ETS," Economic Modelling, Elsevier, vol. 29(3), pages 884-892.
    19. Yihsu Chen & Jos Sijm & Benjamin Hobbs & Wietze Lise, 2008. "Implications of CO 2 emissions trading for short-run electricity market outcomes in northwest Europe," Journal of Regulatory Economics, Springer, vol. 34(3), pages 251-281, December.
    20. Alberola, Emilie & Chevallier, Julien & Cheze, Benoi^t, 2008. "Price drivers and structural breaks in European carbon prices 2005-2007," Energy Policy, Elsevier, vol. 36(2), pages 787-797, February.
    21. Yu, Jongmin & Mallory, Mindy L., 2014. "Exchange rate effect on carbon credit price via energy markets," Journal of International Money and Finance, Elsevier, vol. 47(C), pages 145-161.
    22. Benz, Eva & Trück, Stefan, 2009. "Modeling the price dynamics of CO2 emission allowances," Energy Economics, Elsevier, vol. 31(1), pages 4-15, January.
    23. Wei-Xing Zhou, 2009. "The components of empirical multifractality in financial returns," Papers 0908.1089,, revised Oct 2009.
    24. Kara, M. & Syri, S. & Lehtila, A. & Helynen, S. & Kekkonen, V. & Ruska, M. & Forsstrom, J., 2008. "The impacts of EU CO2 emissions trading on electricity markets and electricity consumers in Finland," Energy Economics, Elsevier, vol. 30(2), pages 193-211, March.
    25. Gil-Alana, Luis A. & Gupta, Rangan & de Gracia, Fernando Perez, 2016. "Modeling persistence of carbon emission allowance prices," Renewable and Sustainable Energy Reviews, Elsevier, vol. 55(C), pages 221-226.
    26. Balcılar, Mehmet & Demirer, Rıza & Hammoudeh, Shawkat & Nguyen, Duc Khuong, 2016. "Risk spillovers across the energy and carbon markets and hedging strategies for carbon risk," Energy Economics, Elsevier, vol. 54(C), pages 159-172.
    27. Hammoudeh, Shawkat & Nguyen, Duc Khuong & Sousa, Ricardo M., 2014. "Energy prices and CO2 emission allowance prices: A quantile regression approach," Energy Policy, Elsevier, vol. 70(C), pages 201-206.
    28. Yu, Lean & Li, Jingjing & Tang, Ling & Wang, Shuai, 2015. "Linear and nonlinear Granger causality investigation between carbon market and crude oil market: A multi-scale approach," Energy Economics, Elsevier, vol. 51(C), pages 300-311.
    29. Reboredo, Juan C., 2014. "Volatility spillovers between the oil market and the European Union carbon emission market," Economic Modelling, Elsevier, vol. 36(C), pages 229-234.
    30. Conrad, Christian & Rittler, Daniel & Rotfuß, Waldemar, 2012. "Modeling and explaining the dynamics of European Union Allowance prices at high-frequency," Energy Economics, Elsevier, vol. 34(1), pages 316-326.
    31. Maria Mansanet-Bataller & Angel Pardo & Enric Valor, 2007. "CO2 Prices, Energy and Weather," The Energy Journal, International Association for Energy Economics, vol. 0(Number 3), pages 73-92.
    32. da Silva, Patricia Pereira & Moreno, Blanca & Figueiredo, Nuno Carvalho, 2016. "Firm-specific impacts of CO2 prices on the stock market value of the Spanish power industry," Energy Policy, Elsevier, vol. 94(C), pages 492-501.
    33. Emilie Alberola & Benoît Chèze & Julien Chevallier, 2008. "The EU Emissions Trading Scheme : Disentangling the Effects of Industrial Production and CO2 Emissions on Carbon Prices," EconomiX Working Papers 2008-12, University of Paris Nanterre, EconomiX.
    34. Kim, Hyun Seok & Koo, Won W., 2010. "Factors affecting the carbon allowance market in the US," Energy Policy, Elsevier, vol. 38(4), pages 1879-1884, April.
    35. Delarue, Erik & Lamberts, Hans & D’haeseleer, William, 2007. "Simulating greenhouse gas (GHG) allowance cost and GHG emission reduction in Western Europe," Energy, Elsevier, vol. 32(8), pages 1299-1309.
    36. repec:dau:papers:123456789/4210 is not listed on IDEAS
    37. Tan, Xue-Ping & Wang, Xin-Yu, 2017. "Dependence changes between the carbon price and its fundamentals: A quantile regression approach," Applied Energy, Elsevier, vol. 190(C), pages 306-325.
    38. Pal, Mayukha & Madhusudana Rao, P. & Manimaran, P., 2014. "Multifractal detrended cross-correlation analysis on gold, crude oil and foreign exchange rate time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 416(C), pages 452-460.
    39. Zhu, Huijian & Zhang, Weiguo, 2018. "Multifractal property of Chinese stock market in the CSI 800 index based on MF-DFA approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 490(C), pages 497-503.
    40. Zhang, Yue-Jun, 2011. "The impact of financial development on carbon emissions: An empirical analysis in China," Energy Policy, Elsevier, vol. 39(4), pages 2197-2203, April.
    41. Boersen, Arieke & Scholtens, Bert, 2014. "The relationship between European electricity markets and emission allowance futures prices in phase II of the EU (European Union) emission trading scheme," Energy, Elsevier, vol. 74(C), pages 585-594.
    42. Cao, Guangxi & Zhang, Minjia & Li, Qingchen, 2017. "Volatility-constrained multifractal detrended cross-correlation analysis: Cross-correlation among Mainland China, US, and Hong Kong stock markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 472(C), pages 67-76.
    43. B. Podobnik & I. Grosse & D. Horvatić & S. Ilic & P. Ch. Ivanov & H. E. Stanley, 2009. "Quantifying cross-correlations using local and global detrending approaches," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 71(2), pages 243-250, September.
    44. Cao, Guangxi & Xu, Wei, 2016. "Nonlinear structure analysis of carbon and energy markets with MFDCCA based on maximum overlap wavelet transform," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 444(C), pages 505-523.
    45. Daskalakis, George & Psychoyios, Dimitris & Markellos, Raphael N., 2009. "Modeling CO2 emission allowance prices and derivatives: Evidence from the European trading scheme," Journal of Banking & Finance, Elsevier, vol. 33(7), pages 1230-1241, July.
    46. Gvozdanovic, Igor & Podobnik, Boris & Wang, Duan & Eugene Stanley, H., 2012. "1/f behavior in cross-correlations between absolute returns in a US market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(9), pages 2860-2866.
    47. Dutta, Srimonti & Ghosh, Dipak & Chatterjee, Sucharita, 2016. "Multifractal detrended Cross Correlation Analysis of Foreign Exchange and SENSEX fluctuation in Indian perspective," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 463(C), pages 188-201.
    48. Cao, Guangxi & Xu, Longbing & Cao, Jie, 2012. "Multifractal detrended cross-correlations between the Chinese exchange market and stock market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(20), pages 4855-4866.
    49. Zhuang, Xiaoyang & Wei, Yu & Zhang, Bangzheng, 2014. "Multifractal detrended cross-correlation analysis of carbon and crude oil markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 399(C), pages 113-125.
    50. Zhu, Lei & Zhang, Xiao-Bing & Li, Yuan & Wang, Xu & Guo, Jianxin, 2017. "Can an emission trading scheme promote the withdrawal of outdated capacity in energy-intensive sectors? A case study on China's iron and steel industry," Energy Economics, Elsevier, vol. 63(C), pages 332-347.
    51. Xi-Yuan Qian & Ya-Min Liu & Zhi-Qiang Jiang & Boris Podobnik & Wei-Xing Zhou & H. Eugene Stanley, 2015. "Detrended partial cross-correlation analysis of two nonstationary time series influenced by common external forces," Papers 1504.02435,, revised Apr 2015.
    52. Segnon, Mawuli & Lux, Thomas & Gupta, Rangan, 2017. "Modeling and forecasting the volatility of carbon dioxide emission allowance prices: A review and comparison of modern volatility models," Renewable and Sustainable Energy Reviews, Elsevier, vol. 69(C), pages 692-704.
    53. Ma, Feng & Wei, Yu & Huang, Dengshi, 2013. "Multifractal detrended cross-correlation analysis between the Chinese stock market and surrounding stock markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(7), pages 1659-1670.
    54. Moreno, Blanca & Pereira da Silva, Patrícia, 2016. "How do Spanish polluting sectors' stock market returns react to European Union allowances prices? A panel data approach," Energy, Elsevier, vol. 103(C), pages 240-250.
    55. Wei-Xing Zhou, 2008. "Multifractal detrended cross-correlation analysis for two nonstationary signals," Papers 0803.2773,
    56. Lund, Peter, 2007. "Impacts of EU carbon emission trade directive on energy-intensive industries -- Indicative micro-economic analyses," Ecological Economics, Elsevier, vol. 63(4), pages 799-806, September.
    57. Veith, Stefan & Werner, Jörg R. & Zimmermann, Jochen, 2009. "Capital market response to emission rights returns: Evidence from the European power sector," Energy Economics, Elsevier, vol. 31(4), pages 605-613, July.
    58. Ruan, Qingsong & Wang, Yao & Lu, Xinsheng & Qin, Jing, 2016. "Cross-correlations between Baltic Dry Index and crude oil prices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 453(C), pages 278-289.
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