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China is the world's largest developing country and a carbon dioxide emitter. A functional carbon market can effectively reduce carbon emissions. This paper uses the Markov chain Monte Carlo-stochastic volatility model and the wavelet multi-resolution model to analyze the volatility of price returns and the dynamic characteristics of price fluctuations in the carbon pilot markets in Hubei, Shanghai, and Shenzhen. The price movements in these markets are compared to the emissions trading system of the European Union (EU-ETS). The results show that there is a volatility clustering in the price of carbon trading in Hubei, Shanghai, Shenzhen and the EU-ETS. China's carbon pilot markets have a deficiency in terms of volatility stability, as does the EU-ETS. From a long-term perspective, China's carbon market lacks a detailed development plan, which is vital because the construction of the market system is not yet optimal. From a short-term view, China's carbon market is not active and the participants' attitude toward risk is extremely sensitive. • MCMC-SV and wavelet multi-resolution model applied to carbon price volatility. • Three major Chinese markets are compared to the EU-ETS. • All markets evidence volatility clustering. • China's carbon market lacks a detailed development plan for the long term. • Short-term, China's carbon market must become more active and offer more products. [ABSTRACT FROM AUTHOR]