The joint behavior of internal and external system brings out a high complexity of the carbon and oil price interactions, such as non-linearity and multi-frequency. This paper innovatively proposed a time-frequency mechanism between carbon and oil markets from the two aspects of internal system and external factors, and introduced a novelty partial wavelet analytics to explore their dynamic multi-scale interactions. We selected the European carbon and Brent oil futures prices data from March 2009 to December 2020, with the consideration of several necessary control variables from the external surroundings. Our findings point to a stable and strong in-phase relationship between the two markets, with oil leading at medium and lower frequencies. However, the mutual leading relationships are especially sensitive during abnormal political events and periods of financial recession and global emergency, which are observed at different periods for intermediate horizons. What is more, the interactions are more diversified and feebler at short-timescale. Under the vision of carbon neutrality, these evidences provide invaluable guidance for regulators to structure a more flexible adjusting mechanism for the risk control of carbon markets, and also help investors to hedge risk aimed at different time horizons.

内部和外部系统的共同行为带来了碳和石油价格相互作用的高度复杂性，例如非线性和多频。本文从内部系统和外部因素两个方面创新性地提出了碳市场与石油市场之间的时频机制，并介绍了新颖的部分小波分析以探讨其动态多尺度相互作用。我们选择了2009年3月至2020年12月的欧洲碳和布伦特原油期货价格数据，并考虑了来自外部环境的几个必要控制变量。我们的发现表明，两个市场之间存在稳定而牢固的同相关系，其中石油处于中低频。然而，在异常的政治事件以及金融衰退和全球紧急情况期间，相互领导关系特别敏感，在中间阶段的不同时期观察到这种情况。而且，交互作用在短时间范围内更加多样化和灵活。在碳中和的视野下，这些证据为监管机构构建更灵活的碳市场风险控制调整机制提供了宝贵的指导，还有助于投资者对冲不同时间段的风险。