An improved GM(1,1) model based on weighted MSE and optimal weighted background value and its application

GM(1,1) model is widely used because it does not require a large number of samples and has a low computational complexity and no limitation of statistical assumptions. Common drawback of the GM(1,1) models developed by various techniques for improving the performance is their unsatisfied predicting accuracy although they have satisfied fitting accuracy. The aim of this paper is to develop GM(1,1) model with excellent predicting accuracy rather than fitting one. We proposed an improved GM(1,1) model based on weighted mean squared error (MSE) and optimal weighted background value: OB-WMSE-GM(1,1). To illustrate its effectiveness, it was applied to one simulation example and two application examples. For the exponential function simulation example, the fitting MSE, fitting WMSE and predicting MSE of the proposed GM(1,1) (0.000002, 0.000039 and 0.015485) were much lower than ones of the typical GM(1,1) (0.001492, 0.002606 and 1.144524). For the annual LCD TV output prediction example, the fitting MSE, fitting WMSE and predicting MSE of the proposed GM(1,1) (1.425255, 3.199446 and 132.046775) were much lower than ones of the typical GM (1,1) (48.003290, 111.431942 and 5519.135753). For the crude oil processing volume prediction example, the fitting MAPE, fitting WMRE and predicting MAPE of the proposed GM(1,1) (4.090405, 3.213106 and 3.775669) were lower than ones of the typical GM(1,1) (4.399448, 3.883765 and 5.040509). When the proposed method is properly combined with the other various techniques including metabolic mechanism, residual GM(1,1), original sequence pre-processing, background value reconstruction and initial condition optimization, its performance may be more and more improved.