Carbon price interval prediction by bidirectional long short-term memory and multi-objective optimization with an asymmetric scaling approach

Accurate carbon price prediction is essential for decision-making and risk management. Most existing predictive models produce deterministic results and fail to account for uncertainties in carbon prices. To address this limitation, this study introduces an interval prediction framework that effectively captures uncertainties and enhances predictive performance. The proposed framework integrates eXtreme Gradient Boosting (XGBoost) for feature selection, a Modified Scaling Approach (MSA) to generate asymmetric prediction intervals and an improved Non-Dominated Sorting Genetic Algorithm-II (NSGA-II) to determine the optimal scaling parameters. Finally, a Bidirectional Long Short-Term Memory (BiLSTM) network is employed to generate the final interval prediction results. Experiments show that the presented framework outperforms benchmark models and demonstrates robustness.