Grey Discrete GM(1,1) Optimization Model And Its Application

With the progress of society and the development of science and technology,large data age has come,but life often encounter a type of data,the number of samples is small,the information is poor,because the amount of data less,the large data analysis method can not be analyzed Small sample data makes the future of these data difficult to predict.The gray forecasting system solves the research problem of this kind of "small sample" and "poor information",and is widely used in many aspects such as military,biology,medicine,society and so on.The researchers have made extensive research on the gray prediction model,the core GM(1,1)model has been optimized and improved,and various new prediction models have been developed,improved The simulation accuracy of gray prediction and the applicability of the model is extended.In this paper,the original GM(1,1)model is expounded and its defects are analyzed.Under the premise of the original GM(1,1)model,the method of optimizing the background value and selecting the initial value is given.It is verified that the optimization model has white exponential coincidence.Secondly,the discrete gray DGM(1,1)model is introduced,and the improved model of discrete gray DGM(1,1)model is organized,including the approximate nonhomogeneous index NDGM(1,1)model,linear time-varying Parameter model,quadratic time-varying parameter model,three time-varying parameter model,DGM(1,1,m)model,etc.,the relationship between the various improved models and their properties are analyzed,At the same time,the concept of M time-varying parameter model is proposed.Then the ADGM(1,1)model is defined and the model is extended to the ADGM(1,1,m)model.At the same time,it is proved that the ADGM(1,1,m)model can predict the periodic data better.Finally,the model is upgraded to the ZDGM(1,1,m)combination model,the general form of the model and the modeling and forecasting steps are given,and the validity of the ZDGM(1,1,m)combination model is verified by the actual data of the stock.The precision of the three kinds of stock data is simulated,and the future short-term fluctuation is predicted.The results show that the ZDGM(1,1,m)combination model can fit the stock data with complex trend and can be well fitted,and The short-term trend of the forecast also accurately describes the trend of the stock,which shows that the ZDGM(1,1,m)combination model has important practical value.