Correlation analysis of China's carbon market and coal market based on multi-scale entropy

Carbon emission trading is the market-based mechanism to deal with global warming. Energy prices and carbon prices are mutually interacted in a complex way. Correlation analysis of carbon and energy markets can provide valuable information for market participants in both markets. This paper studies the synchronization of carbon market and energy market using sample entropy from multi-scale and cross-over aspects. Piloting carbon markets and the coal market in China are taken as the sample due to the coal-dominant energy structure in this country. To start, we identify 2015 to be the critical year by multi-scale entropy of carbon price and coal price index series. Then we analyze the synchronization between the two markets under particular time scales using cross-sample entropy. This study finds a certain synchronization between carbon and coal markets in China. From the perspective of time scale, we find tau = 20 (one month) is a turning point of time scale for the synchronization. In the long term (longer than one month), the carbon market and the coal market work in a synchrony manner. However, in small scale (shorter than one month), there exists weak synchronization. From the perspective of time, the synchronization is low in 2015. Sliding windows technique verifies these synchronization results. Finally, from the overview perspective, the influence of carbon market to the coal market relies on policies and lasts for about one month. This study suggests that the carbon market needs flexible adjustments to improve synchronization.