Carbon dioxide emission is an important environmental issue, and it has also become an important reference factor for governments to formulate social and economic policies. The objective and accurate prediction of carbon dioxide emissions can provide reference and early warning for the implementation of the government's environmental strategy. The change of the original data of carbon dioxide emissions is S-type, but not saturated S-type. The grey Verhulst model is mainly used to describe the process with saturation state, which is suitable for modeling S-type data series. However, it is found that there are inherent errors and limitations in this model. In this paper, the grey action of the grey Verhulst model is improved, a new action Verhulst model is obtained, and its properties are studied. Finally, the new model is used to predict the carbon dioxide emissions of China and Russia, and ARIMA model is added for comparison. The results show that compared with the original Verhulst model, the simulation and prediction accuracy of the optimized Verhulst model are improved by more than 10%, and the ARIMA model underestimates the carbon dioxide emissions. From the result analysis, China and Russia need to formulate strong energy conservation and emission reduction policies, vigorously develop clean energy industry, and promote green production and lifestyle.

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