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A Decomposition-Integration Framework of Carbon Price Forecasting Based on Econometrics and Machine Learning Methods

Author

Listed:
  • Zhehao Huang

    (Guangzhou Institute of International Finance, Guangzhou University, Guangzhou 510006, China)

  • Benhuan Nie

    (School of Economics and Statistics, Guangzhou University, Guangzhou 510006, China)

  • Yuqiao Lan

    (School of Statistics, Southwestern University of Finance and Economics, Chengdu 611130, China)

  • Changhong Zhang

    (Department of Data Science, George Washington University, Washington, DC 20052, USA)

Abstract

Carbon price forecasting and pricing are critical for stabilizing carbon markets, mitigating investment risks, and fostering economic development. This paper presents an advanced decomposition-integration framework which seamlessly integrates econometric models with machine learning techniques to enhance carbon price forecasting. First, the complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) method is employed to decompose carbon price data into distinct modal components, each defined by specific frequency characteristics. Then, Lempel–Ziv complexity and dispersion entropy algorithms are applied to analyze these components, facilitating the identification of their unique frequency attributes. The framework subsequently employs GARCH models for predicting high-frequency components and a gated recurrent unit (GRU) neural network optimized by the grey wolf algorithm for low-frequency components. Finally, the optimized GRU model is utilized to integrate these predictive outcomes nonlinearly, ensuring a comprehensive and precise forecast. Empirical evidence demonstrates that this framework not only accurately captures the diverse characteristics of different data components but also significantly outperforms traditional benchmark models in predictive accuracy. By optimizing the GRU model with the grey wolf optimizer (GWO) algorithm, the framework enhances both prediction stability and adaptability, while the nonlinear integration approach effectively mitigates error accumulation. This innovative framework offers a scientifically rigorous and efficient tool for carbon price forecasting, providing valuable insights for policymakers and market participants in carbon trading.

Suggested Citation

  • Zhehao Huang & Benhuan Nie & Yuqiao Lan & Changhong Zhang, 2025. "A Decomposition-Integration Framework of Carbon Price Forecasting Based on Econometrics and Machine Learning Methods," Mathematics, MDPI, vol. 13(3), pages 1-31, January.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:3:p:464-:d:1580516
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    as
    1. repec:dau:papers:123456789/6969 is not listed on IDEAS
    2. Zhu, Bangzhu & Ye, Shunxin & Han, Dong & Wang, Ping & He, Kaijian & Wei, Yi-Ming & Xie, Rui, 2019. "A multiscale analysis for carbon price drivers," Energy Economics, Elsevier, vol. 78(C), pages 202-216.
    3. Han, Meng & Ding, Lili & Zhao, Xin & Kang, Wanglin, 2019. "Forecasting carbon prices in the Shenzhen market, China: The role of mixed-frequency factors," Energy, Elsevier, vol. 171(C), pages 69-76.
    4. Lin, Yu & Lu, Qin & Tan, Bin & Yu, Yuanyuan, 2022. "Forecasting energy prices using a novel hybrid model with variational mode decomposition," Energy, Elsevier, vol. 246(C).
    5. Diebold, Francis X & Mariano, Roberto S, 2002. "Comparing Predictive Accuracy," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 134-144, January.
    6. Bao-jun Tang & Pi-qin Gong & Cheng Shen, 2017. "Factors of carbon price volatility in a comparative analysis of the EUA and sCER," Annals of Operations Research, Springer, vol. 255(1), pages 157-168, August.
    7. Cogoljević, Dušan & Alizamir, Meysam & Piljan, Ivan & Piljan, Tatjana & Prljić, Katarina & Zimonjić, Stefan, 2018. "A machine learning approach for predicting the relationship between energy resources and economic development," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 495(C), pages 211-214.
    8. Byun, Suk Joon & Cho, Hangjun, 2013. "Forecasting carbon futures volatility using GARCH models with energy volatilities," Energy Economics, Elsevier, vol. 40(C), pages 207-221.
    9. Zhao, Xin & Han, Meng & Ding, Lili & Kang, Wanglin, 2018. "Usefulness of economic and energy data at different frequencies for carbon price forecasting in the EU ETS," Applied Energy, Elsevier, vol. 216(C), pages 132-141.
    10. Li, Guohui & Ning, Zhiyuan & Yang, Hong & Gao, Lipeng, 2022. "A new carbon price prediction model," Energy, Elsevier, vol. 239(PD).
    11. Chiu, Fan-Ping & Kuo, Hsiao-I. & Chen, Chi-Chung & Hsu, Chia-Sheng, 2015. "The energy price equivalence of carbon taxes and emissions trading—Theory and evidence," Applied Energy, Elsevier, vol. 160(C), pages 164-171.
    12. Tan, Zhongfu & Zhang, Jinliang & Wang, Jianhui & Xu, Jun, 2010. "Day-ahead electricity price forecasting using wavelet transform combined with ARIMA and GARCH models," Applied Energy, Elsevier, vol. 87(11), pages 3606-3610, November.
    13. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    14. Huang, Yumeng & Dai, Xingyu & Wang, Qunwei & Zhou, Dequn, 2021. "A hybrid model for carbon price forecastingusing GARCH and long short-term memory network," Applied Energy, Elsevier, vol. 285(C).
    15. E, Jianwei & Ye, Jimin & He, Lulu & Jin, Haihong, 2019. "Energy price prediction based on independent component analysis and gated recurrent unit neural network," Energy, Elsevier, vol. 189(C).
    16. Chevallier, Julien, 2011. "A model of carbon price interactions with macroeconomic and energy dynamics," Energy Economics, Elsevier, vol. 33(6), pages 1295-1312.
    17. Baris Karapinar & Hasan Dudu & Ozge Geyik & Aykut Mert Yakut, 2020. "How to reach an elusive INDC target: macro-economic implications of carbon taxation and emissions trading in Turkey," Climate Policy, Taylor & Francis Journals, vol. 19(9), pages 1157-1172, July.
    18. Bangzhu Zhu & Ping Wang & Julien Chevallier & Yiming Wei, 2015. "Carbon Price Analysis Using Empirical Mode Decomposition," Computational Economics, Springer;Society for Computational Economics, vol. 45(2), pages 195-206, February.
    19. Yingkai Yin & Zhihui Jiang & Yazhou Liu & Zheng Yu, 2019. "Factors Affecting Carbon Emission Trading Price: Evidence from China," Emerging Markets Finance and Trade, Taylor & Francis Journals, vol. 55(15), pages 3433-3451, December.
    20. Harvey, David & Leybourne, Stephen & Newbold, Paul, 1997. "Testing the equality of prediction mean squared errors," International Journal of Forecasting, Elsevier, vol. 13(2), pages 281-291, June.
    21. Zhu, Bangzhu & Ye, Shunxin & Wang, Ping & He, Kaijian & Zhang, Tao & Wei, Yi-Ming, 2018. "A novel multiscale nonlinear ensemble leaning paradigm for carbon price forecasting," Energy Economics, Elsevier, vol. 70(C), pages 143-157.
    22. Zhu, Bangzhu & Han, Dong & Wang, Ping & Wu, Zhanchi & Zhang, Tao & Wei, Yi-Ming, 2017. "Forecasting carbon price using empirical mode decomposition and evolutionary least squares support vector regression," Applied Energy, Elsevier, vol. 191(C), pages 521-530.
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