The European Union Emissions Trading System (EU ETS) serves as the cornerstone of European climate policy, providing a critical mechanism for mitigating greenhouse gas emissions. Accurate forecasting of the carbon allowance prices within the market is essential for policymakers, enterprises, and investors. To address the need for interval-valued time series modeling and forecasting in the carbon market, this paper proposes a Transformer-based multi-task learning framework that integrates online news and search engine data information to forecast interval-valued EU carbon allowance futures prices. Empirical evaluations demonstrate that the proposed framework achieves superior predictive accuracy for short-term forecasting and remains robust under high market volatility and economic policy uncertainty compared to single-task learning benchmarks. Furthermore, ablation experiments indicate that incorporating news sentiment intensity and search index effectively enhances the framework’s predictive performance. Interpretability analysis highlights the critical role of specific temporal factors, while the time-varying variable importance analysis further underscores the influence of carbon allowance close prices and key energy market variables and also recognizes the contributions of news sentiment. In summary, this study provides valuable insights for policy management, risk hedging, and portfolio decision-making related to interval-valued EU carbon prices and offers a robust forecasting tool for carbon market prediction.

The prediction of agricultural commodity futures returns is crucial for understanding global economic trends, alleviating inflationary pressures, and optimizing investment portfolios. However, current research that uses full-sample decomposition to predict agricultural futures returns suffers from data leakage, and the resulting forecast bias leads to overly optimistic outcomes. Additionally, previous studies have lacked a comprehensive consideration of key economic variables that influence agricultural prices. To address these issues, this study proposes the “Rolling VMD-LASSO-Mixed Ensemble” forecasting framework and compares its performance with “Rolling VMD” against univariate models, “Rolling VMD-LASSO” against “Rolling VMD”, and “Rolling VMD-LASSO-Mixed Ensemble” against “Rolling VMD-LASSO”. Empirical results show that, on average, “Rolling VMD” improved MSE, MAE, Theil U, ARV, and DA by 3.05%, 1.09%, 1.52%, 2.96%, and 11.11%, respectively, compared to univariate models. “Rolling VMD-LASSO” improved these five indicators by 2.11%, 1.15%, 1.09%, 2.13%, and 1.00% over “Rolling VMD”. The decision tree-based “Rolling VMD-LASSO-Mixed Ensemble” outperformed “Rolling VMD-LASSO” by 1.98%, 0.96%, 1.28%, 2.55%, and 4.18% in the five metrics. Furthermore, the daily average return, maximum drawdown, Sharpe ratio, Sortino ratio, and Calmar ratio based on prediction results also show that “Rolling VMD” outperforms univariate forecasting, “Rolling VMD-LASSO” outperforms “Rolling VMD”, and “Rolling VMD-LASSO-Mixed Ensemble” outperforms “Rolling VMD-LASSO”. This study provides a more accurate and robust forecasting framework for the global agricultural futures market, offering significant practical value for investor risk management and policymakers in stabilizing prices.

Existing interval carbon price forecasting methods usually estimate the upper and lower bounds independently or derive them from point forecasts, overlooking their intrinsic coupling and risking logically inconsistent outputs. We propose a constrained multi-task learning framework, CMTL-ATCN, that treats interval-valued carbon prices as coupled tasks and optimizes them jointly under logical consistency constraints. The model uses attention-enhanced temporal convolutional networks (ATCN) to extract shared and task-specific features from multi-source data, which are then fused and decoded through dual task heads; all parameters are optimized jointly with a loss function that adds a logic penalty enforcing agreement between the two bounds. On China’s national (CEA), Guangdong (GDEA), and Hubei (HBEA) carbon markets, CMTL-ATCN attains the lowest interval forecast errors among deep models and eliminates logical inconsistencies entirely with zero violations. The results indicate that the proposed framework is promising for interval-valued forecasting in complex environments.