Interactions among correlations: How does the volatility of the carbon-energy price correlations transmit across different time scales?

Not only do the carbon and energy prices influence each other, but their correlations also affect one another. Revealing the volatility transmission of the carbon-energy price correlations across various scales facilitates a deep understanding of the risk propagation between the two markets. We study the multiscale fluctuation characteristics and the cross-scale volatility transmission of the carbon-energy price correlations. The results show that the volatility spillover between the carbon-energy price correlations is strong in the time-frequency domain. The daily carbon-energy price correlations are the primary source of volatility spillovers. The short-term correlations show a "bidirectional spillover" pattern within the volatility spillover system. The short-term carbon-coal price correlations are the key to volatility risk propagation, and the short-term carbon-oil price correlations play a central role in receiving volatility risks. The longest volatility transmission path shows that the transmission of the correlation fluctuations might be concentrated on certain specific scales. This also highlights the potential for cross-market systemic risks. The strongest transmission path indicates that the semi-monthly carbon-coal correlations are the bridge, and the daily carbon-oil correlations are the most affected factor in the cross-market volatility risk transmission. A periodicity-based reference for decision-making is provided based on these findings.