Augmented fractional accumulation grey model and its application: Class ratio and restore error perspectives

Compared with the traditional first-order accumulation, fractional accumulation is a more efficient data transformation technique, whose order can be determined by the original sequence thus the smoothness and concavity of the data can be effectively improved, but this data-driven property affects the reliability and stability of the prediction while bringing high fitting accuracy. At the same time, the class ratio of the original data and the restore error of the grey model can reflect the degree of matching between the data and the model. Therefore, we summarize a set of methods to study these two perspectives by means of matrix decomposition, function analysis and numerical simulation, and then introduce the augmented fractional accumulation grey model with order optimization constraints. Through empirical test and case analysis, the established model whose modeling process is more rigorous has greater prediction effect and higher modeling efficiency, and can be extended to different fractional accumulated generating operators.