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<p>Extensive explorations have been undertaken regarding carbon price forecasting, particularly in light of the significance of the emission trading system (ETS), one of the most economical strategies for addressing global warming. Nevertheless, current literature primarily emphasizes one-step-ahead carbon price forecasting, with insufficient focus on multi-step predictions that could yield deeper insights for relative decision-makers. This research presents an innovative Step-find DirRec framework utilizing a two-stage data processing methodology to improve the precision of mid-term multi-step forecasting. Initially, data decomposition and reconstruction techniques are employed to mitigate the volatility of the original carbon price series. Then, a data-denoising approach is implemented to reduce the impact of residual noise further. A Step-find algorithm is designed to determine the optimal delays and output lengths for multi-step forecasting. The extreme learning machine, enhanced by a novel cosine-based whale optimization algorithm, is proposed as the foundational forecasting model. Empirical tests on the Shenzhen pilot and China’s national ETS confirm the model’s effectiveness. A comparative assessment of the proposed model against existing prominent models for both one-step-ahead and multi-step-ahead carbon price forecasting validates its superiority. Compared with the recursive structure, the integration of the Step-find DirRec framework with the compared models substantially improves the forecast accuracy with at least 46.58% and at most 80.06% improvement in RMSE, at least 52.95% and at most 80.16% improvement in MAE, and at least 51.00% and at most 82.59% improvement in MAPE. This study also provides suggestions for the application of multi-step carbon price forecasting in the field of thermal unit planning, providing power ancillary services, and power dispatch.</p>

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Multi-step Carbon Price Forecasting: A Novel Step-find DirRec Approach with Evidence from China

  • 期刊论文

  • 发表日期：

    2026年1月9日

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  • Wen Zhang,
  • Deng-Feng Li,
  • Zhibin Wu,
  • Xiao-Jun Zeng

摘要

Extensive explorations have been undertaken regarding carbon price forecasting, particularly in light of the significance of the emission trading system (ETS), one of the most economical strategies for addressing global warming. Nevertheless, current literature primarily emphasizes one-step-ahead carbon price forecasting, with insufficient focus on multi-step predictions that could yield deeper insights for relative decision-makers. This research presents an innovative Step-find DirRec framework utilizing a two-stage data processing methodology to improve the precision of mid-term multi-step forecasting. Initially, data decomposition and reconstruction techniques are employed to mitigate the volatility of the original carbon price series. Then, a data-denoising approach is implemented to reduce the impact of residual noise further. A Step-find algorithm is designed to determine the optimal delays and output lengths for multi-step forecasting. The extreme learning machine, enhanced by a novel cosine-based whale optimization algorithm, is proposed as the foundational forecasting model. Empirical tests on the Shenzhen pilot and China’s national ETS confirm the model’s effectiveness. A comparative assessment of the proposed model against existing prominent models for both one-step-ahead and multi-step-ahead carbon price forecasting validates its superiority. Compared with the recursive structure, the integration of the Step-find DirRec framework with the compared models substantially improves the forecast accuracy with at least 46.58% and at most 80.06% improvement in RMSE, at least 52.95% and at most 80.16% improvement in MAE, and at least 51.00% and at most 82.59% improvement in MAPE. This study also provides suggestions for the application of multi-step carbon price forecasting in the field of thermal unit planning, providing power ancillary services, and power dispatch.