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• The influencing factors of carbon prices in China's carbon market are analysed. • The influencing factors and historical data are combined to predict the carbon price. • The EEMD-BP-ELM model and the CHINAGEM-E model are constructed and combined. Carbon price is one of the core indicators of the carbon market. Making accurate predictions of carbon prices based on insight into the volatility characteristics of the carbon market will not only provide a scientific basis for investors and regulators to make decisions and greatly promote emission reduction, but also effectively promote the healthy development of the carbon financial market. Based on the historical carbon price data of the national carbon market, this paper constructs the EEMD-BP-ELM model to predict the high and low frequency components of China's future carbon price. On this basis, according to China's goal of peaking carbon emissions before 2030 and achieving carbon neutrality before 2060, the CHINAGEM-E model is used to predict the trend component of the carbon price under the baseline and the 2060 carbon neutral scenarios. Finally, the trend component is combined with the high and low frequency components to obtain the price range from 2022 to 2060. We find that under the baseline scenario, China's carbon price range in 2060 is [343, 785] CNY/tCO2, while under the 2060 carbon neutral scenario, this price range is [1543, 3531] CNY/tCO2. [ABSTRACT FROM AUTHOR]