基于反余割函数变换的NGM(1,1)模型及其应用

NGM(1,1)Model Based on Inverse Cosecant Function Transformation and Its Application

针对灰色理论中原始序列光滑性较差的情况,提出了一种基于反余割函数的数据变换方法.首先,结合函数的自身特点,证明了反余割变换具有改善数据光滑性、压缩数据级比、保持数据单调上凹性的性质;然后,与常用的三种变换方法进行比较,证明了其在提高原始序列光滑度上的优越性;最后,构建了基于反余割函数变换的NGM(1,1)模型.经过具体实践,新模型预测结果的平均绝对误差为0.0905,与传统模型相比,拥有较高的拟合及预测精度.

Focused on the case of poor smoothness of the original sequence in the grey theory,a new type of data transformation method based on inverse cosecant function was proposed.Firstly,combined with characteristics of the function,it was proved that the transformation method could improve the smoothness,compress the ratio and maintain the monotonicity and concavity of the original sequence.Then,the data transformation method was compared with the three ones,which proved its superiority in improving the smoothness of the original sequence.Finally,the data transformation method of inverse cosecant was applied to the NGM(1,1)model.Through the specific engineering practice,the average absolute error of the prediction result of the NGM(1,1)model based on the new data transformation is 0.0905.In contrast with the traditional model,it has high fitting and prediction precision.