Linear Transformation Properties of Grey Model

摘要

Linear transformation of data series is a common data processing method, but the related properties of a linear transformation of data series have rarely been theoretically proved. Based on the discrete grey DGM(1,1) model, we wish to investigate the influence of linear transformation on model precision from three aspects: the quasi-smooth of linear transform sequence, the stability, and morbidity of the transform sequence model. It is found that the linear transformation of X-(0) does not destroy its quasi-smoothness, and the scale parameter rho affects the stability of the model but does not change the accuracy of the model. Appropriate position parameter mu can improve the accuracy of the model and reduce the condition number of the matrix. Finally, these results are verified through a case study.