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The integration or segmentation of regional carbon prices implies that barriers may hinder prices from adjusting efficiently and impede linkages between regional carbon markets. Past studies have found that crossregional carbon prices in China tend to diverge, indicating unbalanced regional markets and that carbon cap-and-trade policies may be insufficiently effective. China's carbon trading pilots opened in 2013. Is the integration efficient? This is the research question addressed in this study. This paper uses the carbon prices of four carbon-trading pilot regions in China (i.e. Beijing, Shanghai, Tianjin, and Guangdong) over the period of January 1, 2014, to March 23, 2021, to explore whether prices are correlated across three dimensions: long-term convergence, short-term correlation, and volatility transmission by adopting a vector error correction model with heterogeneous variances. And by using longer-term daily data and empirical tests that can account for the multiple-faceted correlations, this paper provides evidence showing that long-term convergence and risk transfer between the four regional carbon prices exist, which indicates significant regional integration. The results indicate that the price behavior of the Beijing pilot is efficient and that the Shanghai pilot has the lowest volatility. The paper also documents an information transfer pattern. For example, the Beijing pilot is shown to be the leading risk transfer market, whereas the Shanghai pilot is shown to be the market where most risk is transferred. Contrary to findings elsewhere, our main results demonstrate that China's carbon markets exhibit integration efficiency and no imbalance between regions. This may be because the efficiency of China's carbon markets has improved over time. The evidence also implies that if a multi-dimensional correlation has not been considered, it may underestimate the efficiency of regional carbon prices' integration. [ABSTRACT FROM AUTHOR]