A novel grey prediction model with four-parameter and its application to forecast natural gas production in China

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Due to the non-homology problem and the simple structural characteristics, a grey prediction model will have defects in modeling. In this paper, the structure of the GM(1,1,x(1)) model is deformed, and additional parameters are added. A novel four-parameter grey prediction model NFGM(1,1) is established to avoid the non-homology problem. The accumulation order of the NFGM(1,1) model is optimized to enhance its performance. This paper first introduces a nonlinear term and a linear term into the GM(1,1,x(1)) model to compensate for its structural defects, which can enhance the accuracy of the model in modeling complex modeling sequences. Secondly, a simplified basic formula of the model is proposed to estimate its parameters and iteratively establish the model, which can avoid the problem of non-homologous errors during modeling. Then a novel four-parameter grey prediction model NFGM(1,1) is constructed. Thirdly, the unbiasedness of NFGM(1,1) is proved and verified by matrix theory. Fourthly, by optimizing the order of the NFGM(1,1) model, the model is more flexible and adjustable, and a novel fractional-order four-parameter grey prediction model FNFGM(1,1) can be obtained. Finally, the FNFGM(1,1) model is applied to the prediction of natural gas production in China. The model results show that the FNFGM(1,1) model exhibits superior performance compared to the NFGM(1,1), TWGM(1,1), TDGM(1,1), DGM(1,1), and GM(1,1) models, with the mean relative simulation/prediction/comprehensive percentage errors of 0.92%/1.42%/1.07%, respectively. According to the predicted results, China's natural gas production will reach 3542.9 × 108 m3 in 2027 and some relevant policy recommendations are put forwarded.