The carbon market is closely related to fossil energy markets, but few studies focus on the intensity and direction of the time-varying spillover effects, the time delaying and periodicity between the two classes of markets. This paper uses the time-varying vector parameter autoregressive model with stochastic volatility (TVP-VAR-SV model) and impulse response function to study these issues based on the weekly data of European carbon futures prices and three fossil energy (oil, coal, and natural gas) futures prices. The empirical results indicate that: Firstly, there are obvious spillover effects between the carbon market and fossil energy markets, in which the strength and direction are time-varying and asymmetrical. Secondly, as a whole, the coal market has the greatest impact on the carbon market. Finally, the duration of the time-varying spillover effects between the carbon market and fossil energy markets is around three weeks, and the spillover effect diminishes over time. Especially, the time-varying spillover effect is most significant in the case of one-week lag. The above results can provide practical advice for investors, relevant companies and policymakers. Moreover, it can improve the carbon market mechanism to achieve the purpose of emission reduction.

碳市场与化石能源市场密切相关，但是很少有研究关注时变溢出效应的强度和方向，两类市场之间的时间延迟和周期性。本文使用具有随机波动性的时变矢量参数自回归模型（TVP-VAR-SV模型）和脉冲响应函数，基于欧洲碳期货价格和三种化石能源（石油，煤炭和天然气）的每周数据来研究这些问题。天然气）期货价格。实证结果表明：首先，碳市场与化石能源市场之间存在明显的溢出效应，其强度和方向是时变的和不对称的。其次，总体而言，煤炭市场对碳市场的影响最大。最后，碳市场和化石能源市场之间随时间变化的溢出效应的持续时间约为三周，并且随着时间的推移，溢出效应逐渐减弱。尤其是，在滞后一周的情况下，时变溢出效应最为显着。以上结果可为投资者，相关公司和决策者提供实用建议。而且，它可以改善碳市场机制，以达到减排的目的。