EU ETS carbon price forecasting via VMGE-Net: a variational decomposition and channel-aware GRU framework

Daily carbon prices in the European Union Emissions Trading System (EU ETS) exhibit non-stationarity, multi-scale fluctuations, and changes in market regimes, which complicate short-horizon forecasting. This study proposes VMGE-Net, a compact forecasting model that combines Variational Mode Decomposition (VMD), a Gated Recurrent Unit (GRU) encoder, and Efficient Channel Attention (ECA). VMD organizes the target-price sequence permitted under the specified evaluation protocol into frequency-specific components, the GRU encoder models temporal dependencies in the fused mode and covariate sequence, and ECA recalibrates the resulting hidden channels without dimensionality reduction. The empirical analysis uses 1994 daily EU ETS observations collected between January 20, 2017 and March 18, 2026, together with 25 market and engineered predictors. Under the diagnostic full-series VMD setting, VMGE-Net obtained an R² of 0.8834, an RMSE of 2.1009 EUR/ton, an MAE of 1.3639 EUR/ton, and a MAPE of 1.92%. Under stricter expanding-window and 252-trading-day rolling-window VMD protocols, the corresponding R² values were 0.8657 and 0.8587, respectively, and both settings remained more accurate than the raw-sequence GRU benchmark. Ablation, repeated-run, sensitivity, direct multi-step, rolling-backtesting, complexity, paired-significance, and block-permutation analyses indicate that the observed improvement is associated primarily with frequency-aware signal organization, with an additional contribution from lightweight hidden-channel recalibration. These findings support VMGE-Net as a computationally compact approach to short-horizon EU ETS carbon-price forecasting, while its generalizability to other markets and temporal resolutions remains to be examined.