Department of Statistics, Suzhou University of Science and Technology, Suzhou, PR China.
Department of Finance, Suzhou University of Science and Technology, Suzhou, PR China.
PLoS One. 2023 May 18;18(5):e0285460. doi: 10.1371/journal.pone.0285460. eCollection 2023.
The grey prediction is a common method in the prediction. Studies show that general grey models have high modeling precision when the time sequence varies slowly, but some grey models show low modeling precision for the high-growth sequence. The paper researches the grey modeling for the high-growth sequence using the extended nonlinear grey Bernoulli model NGBM(1,1,t⌃p,α). To improve the nonlinear grey Bernoulli model NGBM(1,1,t⌃p,α)'s prediction precision and make data have better adaptability to the model, the paper makes improvements in the following three aspects: (1) the paper improves the accumulated generating sequence of original time sequence, i.e. making a new transformation of traditional accumulated generating sequence; (2) the paper improves the model's structure, extends the grey action and builds an extended nonlinear grey Bernoulli model NGBM(1,1,t⌃p,α); (3) the paper improves the model's background value and uses the value of cubic spline function to approximate the background value. Because the parameters of the new accumulated generating sequence transformed, the nonlinear grey Bernoulli model's time response equation and the background value are optimized simultaneously, the prediction precision increases greatly. The paper builds an extended nonlinear grey Bernoulli model NGBM(1,1,t⌃2,α) using the method proposed and seven comparison models for China's express delivery volume per capita. Comparison results show that the extended nonlinear grey Bernoulli model built with the method proposed has high simulation and prediction precision and shows the precision superior to that of seven comparison models.
灰色预测是预测中的一种常用方法。研究表明，一般的灰色模型在时间序列变化缓慢时具有较高的建模精度，但某些灰色模型在高增长序列时表现出较低的建模精度。本文使用扩展非线性灰色 Bernoulli 模型 NGBM(1,1,t⌃p,α)研究了高增长序列的灰色建模。为了提高非线性灰色 Bernoulli 模型 NGBM(1,1,t⌃p,α)的预测精度，使数据对模型具有更好的适应性，本文从以下三个方面进行了改进：（1）改进原始时间序列的累加生成序列，即对传统累加生成序列进行新的变换；（2）改进模型结构，扩展灰色作用，建立扩展非线性灰色 Bernoulli 模型 NGBM(1,1,t⌃p,α)；（3）改进模型的背景值，使用三次样条函数的值近似背景值。由于新的累加生成序列转换的参数，非线性灰色 Bernoulli 模型的时间响应方程和背景值同时得到优化，预测精度大大提高。本文使用所提出的方法构建了扩展非线性灰色 Bernoulli 模型 NGBM(1,1,t⌃2,α)，并使用七个比较模型对中国人均快递量进行了比较。结果表明，所提出方法构建的扩展非线性灰色 Bernoulli 模型具有较高的模拟和预测精度，优于七个比较模型。
