Abstract: This paper is based on wavelet theory from the perspective of time-frequency domain. It mainly studies the relationship between carbon market, crude oil futures market and stock market of energy industry at home and abroad. The wavelet mode maximum algorithm based on Lipschitz index is used to explore the structural mutation characteristics of the market. The correlation between carbon market and other markets in time-frequency domain is analyzed by multivariate wavelet coherence analysis. Different from previous studies, this paper comprehensively considers the structural changes of carbon markets and the correlation analysis between markets. The results show that the carbon market has multiple points of different types of structural mutations. These structural changes can be triggered by factors such as policy promulgation, changes in the economic situation, market reforms, and geopolitical events. When the structure of carbon market changes, the binary and ternary wavelet coherence between carbon market and other markets are enhanced. The time-frequency domain of the original binary wavelet coherence coefficient shows strong coherence, and the ternary wavelet coherence is also strong. Some specific time-frequency domains that show weak correlation in the binary wavelet coherence coefficients show strong correlation in the ternary wavelet coherence coefficients. The reasons for its enhancement are related to regional factors and the interaction of the third market. This paper extends the application of the signal processing domain analysis method to the study of the sudden change characteristics of market structure and the analysis of market correlation. Combined with financial time series analysis, multiple markets are included in the research scope, and higher precision information is mined.

Key words: carbon market, market structural change, market correlation, wavelet analysis