Carbon Price Forecasting Using a Hybrid Deep Learning Model: TKMixer-BiGRU-SA

作者：Yuhong Li, Nan Yang, Guihong Bi, Shiyu Chen, Zhao Luo, Xin Shen · 发表于：Symmetry · 年份：2025 · DOI：10.3390/sym17060962 · 被引用次数：9 · 研究领域：Atmospheric and Environmental Gas Dynamics、Energy, Environment, Economic Growth、Environmental Impact and Sustainability

As a core strategy for carbon emission reduction, carbon trading plays a critical role in policy guidance and market stability. Accurate forecasting of carbon prices is essential, yet remains challenging due to the nonlinear, non-stationary, noisy, and uncertain nature of carbon price time series. To address this, this paper proposes a novel hybrid deep learning framework that integrates dual-mode decomposition and a TKMixer-BiGRU-SA model for carbon price prediction. First, external variables with high correlation to carbon prices are identified through correlation analysis and incorporated as inputs. Then, the carbon price series is decomposed using Variational Mode Decomposition (VMD) and Empirical Wavelet Transform (EWT) to extract multi-scale features embedded in the original data. The core prediction model, TKMixer-BiGRU-SA Net, comprises three integrated branches: the first processes the raw carbon price and highly relevant external time series, and the second and third process multi-scale components obtained from VMD and EWT, respectively. The proposed model embeds Kolmogorov–Arnold Networks (KANs) into the Time-Series Mixer (TSMixer) module, replacing the conventional time-mapping layer to form the TKMixer module. Each branch alternately applies the TKMixer along the temporal and feature-channel dimensions to capture dependencies across time steps and variables. Hierarchical nonlinear transformations enhance higher-order feature interactions and improve nonlinear mod...