Forecasting Dynamic Correlations Between Carbon, Energy, and Stock Markets Using a BOHB-Optimized Multivariable Graph Neural Network

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.