离散型灰色预测模型的无偏性与自适应性及其应用

Unbiased and Adaptive of Discrete Grey Prediction Model and Its Application

无偏性与自适应性是灰色预测模型的两个重要性质,是研究模型结构及性能的基础。首先,文章以矩阵为工具,从理论上严格证明了两类常见离散灰色预测模型的无偏性。结果表明:双参数离散灰色预测模型DGM(1,1)仅对齐次指数序列具有无偏性,而三参数离散灰色预测模型TDGM(1,1)则对齐次指数/非齐次指数/线性函数序列均具有无偏性。然后,从模型结构角度对TDGM(1,1)模型面向不同特征序列的自适应性进行了分析,验证了模型结构自适应性与无偏性之间的内在联系。最后,应用TDGM(1,1)模型对世界新能源汽车销售量进行建模,并对预测结果进行了比较和分析。本研究对丰富和完善灰色预测理论具有积极意义。

Unbiasedness and self-adaptability are two important properties of grey prediction model and the basis of studying the structure and performance of the model.The existing studies have mostly verified unbiased from the perspective of examples,without strict mathematical proof,and less analysis of the relationship between unbiased and adaptive.Firstly,using matrix theory,the unbiasedness of two kinds of common discrete grey prediction models is strictly proved in theory and verified by homogeneous index/nonhomogeneous index/linear function sequence.The results show that the two parameter discrete grey prediction model DGM(1,1)is unbiased only for the homogeneous exponential sequence,while the three parameter discrete grey prediction model TDGM(1,1)is unbiased for the exponential/non-homogeneous exponential/linear function sequence.Then,the adaptability of TDGM(1,1)to different feature sequences is analyzed from the perspective of model structure,and the internal relationship between self-adaptability and unbiased of model structure is verified.Finally,the TDGM(1,1)model is applied to forecast the world sales of new energy vehicles,and the prediction results are compared and analyzed.This study has positive significance for enriching and perfecting the grey prediction theory.