Enhancing carbon price point-interval multi-step-ahead prediction using a hybrid framework of autoformer and extreme learning machine with multi-factors

As enterprises are obliged to manage their emission allowances and Production Carbon Footprint (PCF) in operation, predictions of the price of carbon emission allowances (referred to as "carbon price" thereafter) become essential for production optimization. Nevertheless, the challenge of forecasting the highly volatile carbon prices while keeping the forecasts understandable has never been overcome in previous studies. Therefore, this paper introduces a hybrid framework to enhance the applicable scopes and interpretability of carbon price predictions. It starts by selecting features using the maximal information coefficient (MIC). Then, features are decomposed by an improved variational mode decomposition (IVMD) and subsequently aggregated based on similar sample entropy. The decomposed components are forecasted by Autoformer, and their predictions are summed to obtain the final result, with errors corrected by extreme learning machine (ELM). The results show that the proposed prediction model exhibits exceptional accuracy spanning three markets, 12 critical spots of trend transition, and 7 price fluctuations caused by regulatory intervention. Meanwhile, it outperforms eight baselines concerning predictive accuracy for multi-step-ahead and interval forecasts, particularly for the next 15-25 days with an R2 of at least 0.99. Furthermore, the features importance analysis explains the impacts of external factors on carbon price and enhances the interpretability of predictions. This work provides a reference for enhanced accurate carbon price forecasting.