Application grey system theory on prediction of Chinese social donation

The aims of this study were to forecast change of Chinese social donation in recent years by grey Verhulst model to find out characteristics of social donation and grey correlation analysis which was proposed by Professor Deng Julong is used to detect of an interpersonal relationship between the number of social donations from oversea and the number of foundations. This paper provides a quantitative method to study the trend of Chinese social donation. Grey system theory has been used into economy, administration, society and other fields. The reason is that grey system theory can deal with partially unknown parameters in a system and predict behavior of unknown system within a small data. So grey system theory is superiority to other ways. In order to improve precise, grey system theory is introduced into social donation to explain the phenomenon of social donation. Grey system theory consists of grey Verhulst model and grey relative degree. There is a distinct difference between grey Verhulst model and linear equation because of grey Verhulst model can greatly eliminate the stimulation error in small data. Therefore the reliability of predictive model for social donation is examined by Grey Verhulst model and a relationship of both variables for soical donation and foundation is demonstrated by grey relative degree in the small data. According to the original data of Chinese social donation from China Civil Affairs' Statistical Yearbook as well as China Civil Affairs' website between 2012 and 2016, the original data of social donation has meet basic condition of prediction because the data with S-shaped curve indicates growth saturation by simulation. Based on law of data fitting, model of social donation is built and make calculation by formula of grey Verhulst model. This way needn't take a leap from difference equation to differential equation and this model is tested by mean relative error, predictive value along with relative error by inverse accumulated generating operation. Briefly speaking, the patterns of social donation will be identified by the following steps to achieve high forecast accuracy in small data. Original sequences are (572.50, 566.40, 604.40, 654.50, 827.00). The new sequences are generated by 1-IAGO (Inverse Accumulated Generating Operation) from the original data sequences for (572.5000, −6.1000, 38.0000, 50.1000, 172.5000). Mean generation with consecutive neighbors is (569.4500, 585.4000, 629.4500, 740.7500). Grey differential equation for LSE (Least-Square Estimation) of parameters vector is a=0.7189 and b=0.0013.