Research And Application Of Residual Error Corrected CGM(1,1)model

In 1982,Deng Julong proposed the grey systems theory.After nearly 40 years of growth,the grey systems theory has formed quite complete theoretical systems,which has brought Chinese original innovation to system science.As the core of grey prediction model,the first-order univariate grey model,referred to as the GM（7）1,1（8）model for short,it can construct the model and make predictions according to a small amount of known information.At present,the GM（7）1,1（8）model and various extension forms have dealt with many practical problems in production and life,and are widely used in many fields such as tourism,transportation,service,energy,and agriculture.Classical GM（7）1,1（8）model have limitations,for which many researchers have improved models from different angles.However,most optimization methods only aim at one aspect to improve and have one sidedness.In view of the above problems,the article first analyzes the GM（7）1,1（8）model mechanism and proposes to combine the composite Cotes’rule in the numerical analysis theory with the grey dynamic sequence model to optimize the background value.At the same time,the optimization parameter C^（9）is obtained by minimizing the square sum of the relative errors between the original non-negative sequence and the simulation sequence.The method to combine them is called CGM（7）1,1（8）model.In this paper,different development coefficients and prediction steps are selected to analyze the applicability of the model.On this basis,residual error corrected CGM（7）1,1（8）model is established（RCCGM（7）1,1（8）model for short）.The availability of RCCGM（7）1,1（8）model are verified by selecting five different kinds of original data,i.e.ascending convex,ascending concave,strictly non-homogeneous,approximately non-homogeneous and strictly homogeneous.Finally,three sets of real data are selected from the National Database:the total population of China at the end of the year from 2001 to 2017,China’s GDP from 2006 to 2016,and China’s scientific research and experimental development expenditures from 2002 to2017.GM（7）1,1（8）model,NGM（7）1,1,k（8）model,NC-4-GM（7）1,1（8）model,CGM（7）1,1（8）model and RCCGM（7）1,1（8）model are used to simulate and predict,which further showes that the average relative error of the RCCGM（7）1,1（8）model is significantly lower than other models.