Using Fourier Series to Improve the Discrete Grey Model (1, 1)

Abstract

Discrete grey model (1, 1) (abbreviates as DGM (1, 1)), is a version of grey forecasting model. Since appeared, its has been attracted by many scientists in dealing with the problem related to uncertainly information and small sample data. In recent years, this model has been improved the accuracy in forecast by scientifics. However, the existing DGM (1, 1) model cannot be used in some special scenarios such as the significant fluctuation or noise in data. Solving this issue, this paper propose a novel grey forecasting model named as Fourier Discrete Grey Model (1, 1) (abbreviated as F-DGM (1, 1)). This model was built by combined the Fourier series and DGM (1, 1) model. Through the example in Xie and Liu’s paper (Xie and Liu [28]) and practical application, these simulation outcomes demonstrated that the F-DGM (1, 1) model provided remarkable prediction performance compared with the other grey forecasting models. Future direction, the authors will use different equations or different methodologies to improve the DGM (1, 1) model. The other direction is applied the proposed model for dealing with the highly fluctuation data in different industries.