Abstract
Accurate small-sample prediction is an urgent, very difficult, and challenging task due to the quality of data storage restricted in most realistic situations, especially in developing countries. The grey model performs well in small-sample prediction. Therefore, a novel multivariate grey model is proposed in this study, called FBNGM (1, N, r), with a fractional order operator, which can increase the impact of new information and background value coefficient to achieve high prediction accuracy. The utilization of an intelligence optimization algorithm to tune the parameters of the multivariate grey model is an improvement over the conventional method, as it leads to superior accuracy. This study conducts two sets of numerical experiments on CO2 emissions to evaluate the effectiveness of the proposed FBNGM (1, N, r) model. The FBNGM (1, N, r) model has been shown through experiments to effectively leverage all available data and avoid the problem of overfitting. Moreover, it can not only obtain higher prediction accuracy than comparison models but also further confirm the indispensable importance of various influencing factors in CO2 emissions prediction. Additionally, the proposed FBNGM (1, N, r) model is employed to forecast CO2 emissions in the future, which can be taken as a reference for relevant departments to formulate policies.
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The datasets used and/or analyzed during the current study are available from the corresponding author on reasonable request.
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Funding
This work was partly supported by the National Key Research and Development Program of China (No. 2023YFB3308903), the Humanities and Social Sciences of Ministry of Education Planning Fund (No. 22YJA910004 and No. 22YJCZH028), the Soft Science Project of Shaanxi Province Fund (No. 2022KRM093), and the Fundamental Research Funds for the Central Universities Fund (No. SK2022040).
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Yan Xu: supervision, writing, review, and editing. Tong Lin: conceptualization, software, writing — original draft. Pei Du: conceptualization, methodology, supervision, writing, review, and editing. Jianzhou Wang: validation, formal analysis.
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Xu, Y., Lin, T., Du, P. et al. The research on a novel multivariate grey model and its application in carbon dioxide emissions prediction. Environ Sci Pollut Res 31, 21986–22011 (2024). https://doi.org/10.1007/s11356-024-32262-9
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DOI: https://doi.org/10.1007/s11356-024-32262-9