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Open AccessArticle
Forecasting Dynamic Correlations Between Carbon, Energy, and Stock Markets Using a BOHB-Optimized Multivariable Graph Neural Network
by
Qianli Ma
Qianli Ma 1,2 and
Meng Han
Meng Han 1,*
1
Bay Area International Business School, Beijing Normal University, Zhuhai 519087, China
2
School of Data Science, The Chinese University of Hong Kong, Shenzhen, Shenzhen 518172, China
*
Author to whom correspondence should be addressed.
Mathematics 2026, 14(1), 171; https://doi.org/10.3390/math14010171 (registering DOI)
Submission received: 12 November 2025
/
Revised: 28 December 2025
/
Accepted: 30 December 2025
/
Published: 1 January 2026
Abstract
Accurately forecasting the dynamic linkages among carbon, energy, and stock markets is essential for effective risk management and the design of energy transition strategies. This study proposes a BOHB-optimized Multivariable Graph Neural Network (BOHB-MSGNN) framework to forecast dynamic correlations derived from a DCC-GARCH model. Using data from the EU ETS market and related energy and stock markets, we document strong and persistent interconnectedness across markets, with the carbon market exhibiting the closest linkage to natural gas, followed by coal, stocks, and oil. Moreover, the proposed BOHB-MSGNN model significantly outperforms benchmark models in predicting dynamic risk correlations across multiple error metrics, owing to its ability to capture both intra-series and inter-series dependencies. Minimum-variance portfolios based on predicted correlations achieve returns similar to those using realized correlations. Forecasts also suggest a moderate decline in future correlations, highlighting diversification opportunities. These results offer practical implications for portfolio allocation, risk management, and carbon market policy.
Share and Cite
MDPI and ACS Style
Ma, Q.; Han, M.
Forecasting Dynamic Correlations Between Carbon, Energy, and Stock Markets Using a BOHB-Optimized Multivariable Graph Neural Network. Mathematics 2026, 14, 171.
https://doi.org/10.3390/math14010171
AMA Style
Ma Q, Han M.
Forecasting Dynamic Correlations Between Carbon, Energy, and Stock Markets Using a BOHB-Optimized Multivariable Graph Neural Network. Mathematics. 2026; 14(1):171.
https://doi.org/10.3390/math14010171
Chicago/Turabian Style
Ma, Qianli, and Meng Han.
2026. "Forecasting Dynamic Correlations Between Carbon, Energy, and Stock Markets Using a BOHB-Optimized Multivariable Graph Neural Network" Mathematics 14, no. 1: 171.
https://doi.org/10.3390/math14010171
APA Style
Ma, Q., & Han, M.
(2026). Forecasting Dynamic Correlations Between Carbon, Energy, and Stock Markets Using a BOHB-Optimized Multivariable Graph Neural Network. Mathematics, 14(1), 171.
https://doi.org/10.3390/math14010171
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