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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

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    Cited by:

    1. Ting Yao & Charbel Salloum & Yong Jiang & Yi‐Shuai Ren, 2026. "Can Attention Mechanisms Improve Carbon Price Forecasting Accuracy?," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 45(1), pages 156-178, January.
    2. Yongfa Chen & Yingjie Zhu & Jie Wang & Meng Li, 2025. "A Hybrid Model for Carbon Price Forecasting Based on Secondary Decomposition and Weight Optimization," Mathematics, MDPI, vol. 13(14), pages 1-24, July.
    3. Giorgos Kotsompolis & Panagiotis Cheilas & Konstantinos N. Konstantakis & Evangelos Sfakianakis & Stephane Goutte & Panayotis G. Michaelides, 2026. "Smart Forecasting of Carbon Prices Using Machine Learning and Neural Networks: When ARIMA Meets XGBoost and LSTM," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 45(1), pages 47-60, January.

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