Correlation and causality between carbon and energy markets: a complexity perspective

Global warming obliges humans to focus on the relationships between carbon and energy markets. This study considers the relationship between carbon and energy markets from a complexity perspective. Chinese carbon prices and four energy indexes are selected as empirical variables. First, the complexities of carbon and energy markets are measured by multi-scale fuzzy entropy. The critical time delay of the series is then obtained by maximizing the Pearson coefficients between these markets. Further, analysis of the detrended cross-correlation coefficient confirms the existence of time delay. Finally, transfer entropy is applied to investigate the causality pertaining to dynamic complexity. Results of fuzzy entropy analysis reveal that the carbon market has lower complexity than energy markets. Meanwhile, multi-scale results indicate greater complexity on the small time scales in all markets than on the large time scales. The critical time delay is found to be about 50, which maximizes the correlation coefficient. Finally, causality between carbon and energy markets varies. Expectations in the carbon market impact oil gas and coal markets; electricity and new energy affect the carbon market; and cross-causality exists in the relationship between coal and carbon markets. The participants should focus on the information transmission between carbon and energy markets.