A monotonic multi-output mixed-frequency quantile regression neural network for carbon price prediction

Abstract

Accurate carbon price prediction is crucial for market trading and policy-making. Existing research is mostly based on point prediction using single-frequency data, which makes it difficult to utilize high-frequency information and effectively characterize price uncertainty. Therefore, this study proposes a novel monotonic multi-output mixed-frequency quantile regression neural network model (MMQRGRU-MIDAS). Firstly, this study employs the Least Absolute Shrinkage and Selection Operator (LASSO) method to select key influencing factors from three major categories of variables: energy commodities, financial market indicators, macroeconomic indicators. And introduce the Mixed Data Sampling Regression (MIDAS) module to directly model the original mixed-frequency data, avoiding information loss caused by interpolation or co frequency processing. Furthermore, multi-output structure with monotonicity constraints is designed, and regularization term is added to the loss function to solve the quantile crossing problem in multi quantile joint prediction. Finally, the Gated Recurrent Unit (GRU) module is combined to capture the nonlinear dynamic characteristics of carbon price time series. Empirical studies on two pilot carbon markets in Guangzhou and Hubei have shown that the proposed MMQRGRU-MIDAS model outperforms other comparative models in both point and interval prediction tasks. And the model solves the quantile crossing problem with zero cross loss and cross rate. The results validate the superiority of the proposed model in forecasting accuracy, interval quality, and computational efficiency, providing an effective analytical tool for carbon market risk management and market analysis.

The authors' abstract, as published at the source. Engineering Applications of Artificial Intelligence, 2026 · DOI ↗