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This paper constructs a novel stress measurement system of carbon market from the perspective of trading, emission reduction, and external shocks and simulates the stress indices of national and pilot carbon markets of China with the methods of functional data analysis and criteria importance through intercriteria correlation. It concludes that the overall carbon market stress is in the shape of "W" and still at a high level, with frequent fluctuations and an upward trend. In addition, the stress of Hubei, Beijing, and Shanghai carbon market fluctuates and rises, while the stress of Guangdong carbon market decreases. Moreover, carbon market stress mainly comes from trading and emission reduction. Furthermore, stress fluctuation of Guangdong and Beijing carbon market is more prone to "big waves," indicating that the two markets are sensitive to big events. Finally, the pilot carbon markets are divided into stress-driven and stress-release market and the type of which keeps change in different period. [ABSTRACT FROM AUTHOR]