Carbon market and green bond market are important institutional innovations for reducing greenhouse gas emissions and realizing low-carbon economic transformation. Accurately understanding the characteristics and correlations of the two markets is of great significance for promoting the realization of the goals of “carbon peaking and carbon neutrality”. From the multiple perspectives of time scales and market conditions

the maximum overlap discrete wavelet transform(MODWT) is chosen to decompose the price time series data of China's carbon market and green bond market. Besides

the quantile Granger causality test is used to measure the causal relationship between two markets at different quantiles. Moreover

the association between the two is estimated based on the quantile-to-quantile regression method(QQR). The empirical results show that

China's carbon market is always the Granger reason for the green bond market on various time scales. In short term

when the two markets are both in a bear market or a bull market at the same time

the carbon market has a positive impact on the green bond market

while when one markets is in a bear market and the other is in a bull market

the carbon market has a negative impact on the green bond market. In medium term

the two markets still retain the same correlation as in the short term

but under normal market conditions

the positive impact of the carbon market on the green bond market becomes prominent. In long term

the impact of the carbon market on the green bond market has an inverted U-shaped relationship with the green bond market conditions

and there is a sudden change of “negative-positive-negative”.