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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 beimproved. This paper proposes a novel discrete GM(1,1) model, named ${\rmGM_{SD}}$(1,1) model, of which the background value is reconstructed usingSimpson formula. The expression of the specific time response function isdeduced, and the relationship between our model} and the continuous GM(1,1)model with Simpson formula called ${\rm GM_{SC} }$(1,1) model is systematicallydiscussed. The proposed model is proved to be unbiased to simulate thehomogeneous exponent sequence. Further, some numerical examples are given tovalidate the accuracy of the new ${\rm GM_{SD}}$(1,1) model. Finally, thismodel is used to predict the Gross Domestic Product and the freightage ofLanzhou, and the results illustrate the ${\rm GM_{SD}}$(1,1) model providesaccurate prediction.

Improved GM(1,1) model based on Simpson formula and its applications