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Developing more effective carbon mitigation strategies requires accurate forecasting of carbon emissions. This is especially true for China, the United States and India, which produce over half of the world's carbon emissions. China, the United States, and India represent three different types of carbon emissions data. The first data type is typical for China: rapid grows which is thereafter slowing down. The US carbon emissions data show volatile growth and decline. The third data type is common for India's data: accelerated growth. To deal with the volatility of the data and to improve the forecasting accuracy, this paper combines Metabolic Nonlinear Grey Model (MNGM) with Autoregressive Integrated Moving Average (ARIMA) to develop the combined MNGM-ARIMA model, and MNGM with Back Propagation Neural Network (BPNN) to develop the new combined MNGM-BPNN model. In this way, ARIMA and BPNN could correct the modelling residual error of MNGM, to decrease the forecasting error. Through the quantitative data study of the countries in focus, we have made the following findings: First, the mean relative percent errors of the proposed MNGM-ARIMA and MNGM-BPNN models are 1.35% and 1.57%, which are lower than the traditional MNGM, ARIMA, and BPNN models. Besides, it is projected that during the period of 2019–2030, the US′ carbon emissions will keep a downward trend, while carbon emissions in China and India will continue to grow. Finally yet importantly, in the future periods of time, the carbon emissions growth rate in India will be faster than that for China. The above findings have led us to the following conclusions: (1) Error values of those two proposed approaches have proven that the strategy of correcting the forecasting error of the previous models with the latter models can effectively improve the forecasting accuracy. (2) The proposed two combined forecasting techniques have shown sound performance for the three types of data. It is reasonable to believe that new approaches will help to improve insight into better forecasting carbon emissions in other countries and regions of the world. (3) China and India will remain the major sources of global carbon emissions, and should therefore continue their efforts on carbon emission reduction. Image 10221 • China, the United States and India contribute half of global carbon emissions. • Forecasting the carbon emissions is conducive to global carbon emission reduction. • Strategy of "error correction + quadratic modeling" and new models are proposed. • Mean relative errors of the two proposed models achieved 1.35% and 1.57%. • Future carbon emissions growth will be concentrated in developing countries. [ABSTRACT FROM AUTHOR]