Difference-ratio-based NDGM interpolation forecasting algorithm and its application

A difference-ratio-based imputation algorithm is proposed to tackle missing values in modeling sequence and improve prediction accuracy of non-homogenous discrete grey model (NDGM). It is proved that the classical conditions of quasi-smooth sequences are not sufficient and necessary conditions for non-homogenous sequence and a new method is put forward to judge the smoothness of sequences. Reconstruction error of missing value comes from average generation and its impacts on forecasting accuracy of NDGM are also discussed. Compared with average generation, it is also proved that the new method is more effective. Unbiased imputation and prediction of non-homogenous sequence can be realized under this algorithm. Furthermore, two cases are employed to demonstrate that the algorithmic approach is suitable for short-term prediction of sequences characterized by high increasing tendency, insufficient information and outlier value inclusion.