Improved GM(1,1) Model Based on Simpson Formula and Its Applications

标题: Improved GM(1,1) Model Based on Simpson Formula and Its Applications

作者: Ma, Xin ; Wu, Wenqing ; Zhang, Yuanyuan

来源出版物: JOURNAL OF GREY SYSTEM

出版时间: 2019

作者关键词: Grey Forecasting；GM(SD) (1,1) Model；Simpson Formula；Small Sample；Background Value

研究方向: Mathematics

第一地址: 西南科技大学

入藏号：WOS:000509004700003

中国科学院文献情报中心期刊分区： 数学4区

摘要：

The classical GM(1,1) model is an efficient tool to make accurate forecasts with limited samples. But the accuracy of the GM(1,1) model still needs to be improved This paper proposes a novel discrete GM(1,1) model, named GM(SD)(1,1) model, of which the background value is reconstructed using the Simpson formula. The expression of the specific time response function is deduced, and the relationship between our model and the continuous GM(1,1) model with Simpson formula called GM(SC)(1,1) model is systematically discussed. The proposed model is proved to be unbiased to simulate the homogeneous exponent sequence. Further, some numerical examples are given to validate the accuracy of the new GM(SD)(1,1) model. Finally, this model is used to predict the Gross Domestic Product and the freightage of Lanzhou, and the results illustrate the GM(SD)(1,1) model provides accurate prediction.