A novel multi-variable grey forecasting model and its application in forecasting the amount of motor vehicles in Beijing
A novel multi-variable grey forecasting model and its application in forecasting the amount of motor vehicles in Beijing
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一种新型多变量灰色预测模型及其在北京市机动车保有量预测中的应用
DOI：
10.1016/j.cie.2016.10.009
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发表时间：
2016-11
影响因子：
7.9
通讯作者：
Sifeng Liu
中科院分区：
文献类型：
--
作者：
Bo Zeng;Chengming Luo;Chuan Li;Sifeng Liu
GM（1，N）模型的结构缺陷是其模拟预测性能不高的主要原因。针对这一问题，本文在GM（1，N）模型中引入线性修正项h1（k-1）和灰色作用量h2，对模型结构进行了改进。具体来说，h1（k-1）反映因变量与自变量之间的线性关系，h2表示因变量序列的数据变化规律。在此基础上，提出了一种新的多变量灰色预测模型NGM（1，1）。证明了NGM（1，N）模型的时间响应表达式和最终恢复表达式，优化了NGM（1，N）模型的初始值，编制了NGM（1，N）模型的MATLAB程序。最后应用NGM（1，N）模型对北京市机动车保有量进行了模拟预测。与传统GM（1，N）模型和经典DGM（1，1）模型的平均模拟和预测百分误差分别为4.680%、10.685%和4.411%、11.167%相比，新模型的平均模拟和预测百分误差仅为0.009%和1.149%。结果表明，新模型具有最佳的性能，这证实了结构改进的有效性。
The structure defect of the GM(1,N) model is the major reason for its low simulation and prediction performance. To address this issue, a linear correction itemh1(k− 1) and a grey action quantityh2are introduced into the GM(1,N) model to improve its structure in this paper. Specifically, the ‘h1(k− 1)’ reflects the linear relations between the dependent variable and the independent variables, and the ‘h2’ shows the data change law of the dependent variable sequence. Based on this, a novel multi-variable grey forecasting model, NGM(1,1), is proposed. Furthermore, the NGM(1,N) model’s time-response expression and the final restored expression are proved, its initial value is optimized, and a MATLAB program for building the NGM(1,N) model is developed. Lastly the NGM(1,N) model is applied to simulate and forecast the amount of Beijing’s motor vehicles. The mean relative simulation and prediction percentage errors of the new model are only 0.009% and 1.149%, in comparison with the ones obtained from the traditional GM(1,N) model and the classical DGM(1,1) model, which are 4.680%, 10.685% and 4.411%, 11.167% respectively. The findings show that the new model has the best performance, which confirms the effectiveness of the structure improvement.
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影响因子：
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