An improved GM(1,1) model based on iterative weighted least square criterion parameter estimation

The least square method is used in the traditional grey model to estimate the model's structural parameters, but it has limitations in predicting time series with outliers, and the robustness of the model needs to be modified. Therefore, a new method is proposed to estimate the structural parameters of grey model based on the weighted iterative least square method in order to reduce the sensitivity of the traditional least square method in parameter estimation to improve the robustness of traditional grey GM(1, 1) model and its fitting ability in samples containing sensitive information. The grey RGM(1, 1) model's establishment process is described based on the iterative weighted least squares criterion, and the specific weighted iterative least squares steps are used to estimate structural parameters. A state grid company's equipment maintenance cost prediction shows that robust GM(1, 1) has a higher prediction accuracy than the traditional GM(1, 1) grey model. In this paper, the iterative weighted least squares algorithm of structural parameters expands the statistical connotation of grey theory to a certain extent.