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Urbanization and the release of carbon emission are two significant features of contemporary economic and social progress in China. However, there are few studies that consider how urbanization policy goals affect carbon emission. This paper aims to study the nonlinear effects of urbanization policy goals on carbon emission in 13 cities of the Beijing-Tianjin-Hebei region. In this paper, a multi-dimensional spatial disturbance grey model is proposed. Based on matrix perturbation theory, this paper explores the spatial perturbation bounds of the novel model and verifies that the spatial property of the model is consistent with the viewpoint of the First Law of Geography. Then, the novel model is used to predict the urban carbon emission under different urbanization policy goal scenarios. The results showed that the novel model has spatial regional correlation in spatial region prediction. With the development of urbanization level, carbon emissions show a downward trend in more than 50% of cities from 2022 to 2025. In addition, the improvement of urbanization policy goals will promote the carbon peak time of most cities. The carbon emission intensity will exhibit an inverted U-shaped trend distribution in space. The research results are conducive to providing scientific guidance for the formulation of new-type urbanization policies and helping to achieve the dual carbon goals. • A multi-dimensional spatial disturbance grey model is proposed. • The novel grey model is consistent with the viewpoint of the First Law of Geography. • The spatial distribution of carbon intensity showed an inverted U-shaped pattern. [ABSTRACT FROM AUTHOR]

• An improved singular spectrum decomposition is proposed. • High complexity components are secondarily decomposed to reduce its complexity. • An improved prediction model of optimization algorithm is proposed. • Intelligent weighting strategy is introduced to overcome traditional weighting problem. • A combined prediction model for carbon emission is proposed. Accurate prediction of carbon emission is critical for the development of low-carbon economy. However, most carbon emission prediction studies use a single model with low prediction accuracy, and do not consider the instability of carbon emission. Therefore, this paper proposes a combined prediction model of carbon emission. Firstly, the original data is decomposed by singular spectrum decomposition to obtain a limited amount of singular spectrum components. Secondly, high complexity components are secondarily decomposed by variational mode decomposition. Then, chameleon swarm algorithm and carnivorous plant algorithm are used to train the regularization coefficients and kernel parameters of kernel extreme learning machine and least squares support vector machine respectively, and the trained model is used to predict the decomposition components. Finally, induced ordered weighted averaging operator is used to calculate the weight of single model, and error correction is introduced to further promote the prediction accuracy. The carbon emission data of China and the United States is used to make a prediction experiment. The results indicate that the proposed model is superior to other comparative models in different indexes, which provides a new idea for carbon emission prediction. [ABSTRACT FROM AUTHOR]

• Four time-delay weights structural types are designed by the grey incidence model. • The novel multivariable grey prediction model considering the time-delay periods and time-delay weights is proposed. • The accumulating impact of influencing factors on CO 2 emissions of China's transport sector is measured. CO 2 emissions from the transportation sector occupy an increasingly important proportion in China's carbon dioxide emissions. Measuring the accumulative impact of factors on carbon emissions over time is of great significance for formulating corresponding policies. This paper aims to propose a novel time-delay multivariate grey model to measure the CO 2 emissions' accumulating impact of China's transportation sector. Firstly, the grey incidence model is used to identify time lags between the input and output variables, and also analyze the structure type of time-delay weights. Then, an accumulative time-delay multivariate grey prediction model is developed. In this model, a Gaussian formula is used to discretize the convolution integral of the time response function, and the particle swarm optimization algorithm is employed to determine the optimal weight coefficients. Finally, a case for CO 2 emissions prediction is adopted to test the effectiveness and practicality of this model compared with the alternative models. The results show that the proposed model outperforms other six competing models in accordance with two measuring indices, and suggestions on emissions mitigation are proposed based on the prediction results. [ABSTRACT FROM AUTHOR]