Forecasting of interval carbon price in China based on decomposition-reconstruction-ensemble framework

Accurate prediction of carbon prices is imperative for the effective management of carbon markets and the facilitation of a global transition to green energy. This paper introduces a decomposition-reconstruction-ensemble framework aimed at accurately capturing the fluctuations in interval-valued carbon prices. Traditional decomposition and reconstruction methods encounter difficulties when handling interval carbon prices. To address this, this paper introduces the multivariate variational mode decomposition (MVMD) optimized by the rime-ice optimization algorithm (RIME) and the multi-scale fuzzy dispersion entropy (MFDE) to decompose and reconstruct the carbon price. Next, the multiple kernel-based extreme learning machine (MKELM), enhanced by the RIME algorithm, is innovatively introduced to predict each sub-series, incorporating external factors containing energy, economy, and environment that influence carbon prices. Ultimately, all predictions of the sub-series are aggregated to derive the forecasts of the interval carbon price. Empirical analysis reveals that the proposed model surpasses the benchmark approaches in both prediction accuracy and robustness, suggesting its suitability for interval value prediction in intricate scenarios.