Abstract Existing research on carbon price forecasting has predominantly focused on deterministic point forecasts. However, interval forecasting offers richer informational content for decision-makers and facilitates more effective risk management in practical applications. To address this gap, this paper proposes a novel interval prediction model that integrates a Quality-Driven Lower Upper Bound Estimation (QD-LUBE) framework with a decomposition-ensemble methodology. The proposed approach overcomes the inherent limitations of conventional LUBE by adopting a differentiable loss function derived from rigorous statistical principles, thereby enabling efficient neural network optimization via gradient descent. Subsequently, Variational Mode Decomposition (VMD) is employed to separate the original price series into a low-frequency trend component and a high-frequency residual component. Within the QD-LUBE framework, a Multilayer Perceptron (MLP) is utilized to predict the trend, while a Bidirectional Gated Recurrent Unit (Bi-GRU) is designed capture the dynamics of the residuals. The integration of these two outputs yield refined interval forecasts. Finally, the effectiveness of the proposed model is validated utility is further demonstrated through a simple trend-based trading strategy, underscoring the economic value of incorporating uncertainty quantification into carbon trading decisions.
Zhang et al. (Fri,) studied this question.