Currently European Union Allowances (EUA) and secondary Certified Emission Reduction (sCER) have become two dominant carbon trading assets for investors and their linkage attracts much attention from academia and practitioners in recent years. Under this circumstance, we use the empirical mode decomposition (EMD) approach to decompose the two carbon futures contract prices and discuss their correlation from the multi-frequency perspective. The empirical results indicate that, first, the EUA and sCER futures price movements can be divided into those triggered by the long-term, medium-term and short-term market impacts. Second, the price movements in the EUA and sCER futures markets are primarily caused by the long-term impact, while the short-term impact can only explain a small fraction. Finally, the long-term (short-term) effect on EUA prices is statistically uncorrelated with the short-term (long-term) effect of sCER prices, and there is a medium or strong lead-and-lag correlation between the EUA and sCER price components with the same time scales. These results may provide some important insights of price forecast and arbitraging activities for carbon futures market investors, analysts and regulators.