On novel grey forecasting model based on non-homogeneous index sequence

To solve the problem that traditional grey models were constructed on the hypothesis that the original data sequence is in accord with homogeneous index trend rather than non-homogeneous index trend. A novel grey forecasting model based on non-homogeneous index sequence approximately (abbreviated as NDGM) is proposed. It is proved that the models based on homogeneous index sequence are all special cases that of non-homogeneous index sequence. The recursive function of the NDGM model is proposed and the forecasting precision of the model based on pure non-homogeneous index sequence is discussed and the affine properties of the model are further studied. Finally, one numerical case is used to show the effective results of the proposed model.