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A Hybrid Model for Carbon Price Forecasting Based on Improved Feature Extraction and Non-Linear Integration

Author

Listed:
  • Yingjie Zhu

    (School of Mathematics and Statistics, Changchun University, Changchun 130022, China)

  • Yongfa Chen

    (School of Mathematics and Statistics, Changchun University, Changchun 130022, China)

  • Qiuling Hua

    (Economics School, Jilin University, Changchun 130012, China)

  • Jie Wang

    (School of Mathematics and Statistics, Changchun University, Changchun 130022, China)

  • Yinghui Guo

    (School of Mathematics and Statistics, Changchun University, Changchun 130022, China)

  • Zhijuan Li

    (School of Mathematics and Statistics, Changchun University, Changchun 130022, China)

  • Jiageng Ma

    (School of Mathematics and Statistics, Changchun University, Changchun 130022, China)

  • Qi Wei

    (Graduate School, Changchun University, Changchun 130022, China)

Abstract

Accurately predicting the price of carbon is an effective way of ensuring the stability of the carbon trading market and reducing carbon emissions. Aiming at the non-smooth and non-linear characteristics of carbon price, this paper proposes a novel hybrid prediction model based on improved feature extraction and non-linear integration, which is built on complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN), fuzzy entropy (FuzzyEn), improved random forest using particle swarm optimisation (PSORF), extreme learning machine (ELM), long short-term memory (LSTM), non-linear integration based on multiple linear regression (MLR) and random forest (MLRRF), and error correction with the autoregressive integrated moving average model (ARIMA), named CEEMDAN-FuzzyEn-PSORF-ELM-LSTM-MLRRF-ARIMA. Firstly, CEEMDAN is combined with FuzzyEn in the feature selection process to improve extraction efficiency and reliability. Secondly, at the critical prediction stage, PSORF, ELM, and LSTM are selected to predict high, medium, and low complexity sequences, respectively. Thirdly, the reconstructed sequences are assembled by applying MLRRF, which can effectively improve the prediction accuracy and generalisation ability. Finally, error correction is conducted using ARIMA to obtain the final forecasting results, and the Diebold–Mariano test (DM test) is introduced for a comprehensive evaluation of the models. With respect to carbon prices in the pilot regions of Shenzhen and Hubei, the results indicate that the proposed model has higher prediction accuracy and robustness. The main contributions of this paper are the improved feature extraction and the innovative combination of multiple linear regression and random forests into a non-linear integrated framework for carbon price forecasting. However, further optimisation is still a work in progress.

Suggested Citation

  • Yingjie Zhu & Yongfa Chen & Qiuling Hua & Jie Wang & Yinghui Guo & Zhijuan Li & Jiageng Ma & Qi Wei, 2024. "A Hybrid Model for Carbon Price Forecasting Based on Improved Feature Extraction and Non-Linear Integration," Mathematics, MDPI, vol. 12(10), pages 1-26, May.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:10:p:1428-:d:1389739
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    References listed on IDEAS

    as
    1. Haoran Zhao & Sen Guo, 2023. "Carbon Trading Price Prediction of Three Carbon Trading Markets in China Based on a Hybrid Model Combining CEEMDAN, SE, ISSA, and MKELM," Mathematics, MDPI, vol. 11(10), pages 1-21, May.
    2. Boyce, James K., 2018. "Carbon Pricing: Effectiveness and Equity," Ecological Economics, Elsevier, vol. 150(C), pages 52-61.
    3. 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.
    4. Li, Jingmiao & Liu, Dehong, 2023. "Carbon price forecasting based on secondary decomposition and feature screening," Energy, Elsevier, vol. 278(PA).
    5. 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.
    6. Wang, Jujie & Cui, Quan & He, Maolin, 2022. "Hybrid intelligent framework for carbon price prediction using improved variational mode decomposition and optimal extreme learning machine," Chaos, Solitons & Fractals, Elsevier, vol. 156(C).
    7. Sun, Wei & Zhang, Junjian, 2022. "A novel carbon price prediction model based on optimized least square support vector machine combining characteristic-scale decomposition and phase space reconstruction," Energy, Elsevier, vol. 253(C).
    8. Lin, Boqiang & Jia, Zhijie, 2019. "Impacts of carbon price level in carbon emission trading market," Applied Energy, Elsevier, vol. 239(C), pages 157-170.
    9. Liu, Weiping & Wang, Chengzhu & Li, Yonggang & Liu, Yishun & Huang, Keke, 2021. "Ensemble forecasting for product futures prices using variational mode decomposition and artificial neural networks," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    10. Liu, Haiying & Pata, Ugur Korkut & Zafar, Muhammad Wasif & Kartal, Mustafa Tevfik & Karlilar, Selin & Caglar, Abdullah Emre, 2023. "Do oil and natural gas prices affect carbon efficiency? Daily evidence from China by wavelet transform-based approaches," Resources Policy, Elsevier, vol. 85(PB).
    11. Easwaran Narassimhan & Kelly S. Gallagher & Stefan Koester & Julio Rivera Alejo, 2018. "Carbon pricing in practice: a review of existing emissions trading systems," Climate Policy, Taylor & Francis Journals, vol. 18(8), pages 967-991, September.
    12. Zhou, Feite & Huang, Zhehao & Zhang, Changhong, 2022. "Carbon price forecasting based on CEEMDAN and LSTM," Applied Energy, Elsevier, vol. 311(C).
    13. Zhang, Wen & Wu, Zhibin & Zeng, Xiaojun & Zhu, Changhui, 2023. "An ensemble dynamic self-learning model for multiscale carbon price forecasting," Energy, Elsevier, vol. 263(PC).
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