Improved GM(1,1) model based on Simpson formula and its applications
Abstract
The classical GM(1,1) model is an efficient tool to make accurate forecasts with limited samples. But the accuracy of the GM(1,1) model still needs to be improved. This paper proposes a novel discrete GM(1,1) model, named GMSD(1,1) model, of which the background value is reconstructed using Simpson formula. The expression of the specific time response function is deduced, and the relationship between our model and the continuous GM(1,1) model with Simpson formula called GMSC (1,1) model is systematically discussed. The proposed model is proved to be unbiased to simulate the homogeneous exponent sequence. Further, some numerical examples are given to validate the accuracy of the new GMSD(1,1) model. Finally, this model is used to predict the Gross Domestic Product and the freightage of Lanzhou, and the results illustrate the GMSD(1,1) model provides accurate prediction.