Research And Application Of Oscillation Sequence Prediction Based On GM(1,1) Model

Since the 21^st century,with the continuous development of big data and artificial intelligence,it is more and more important to use mathematical model to model and predict variables,and grey theory is a very important theory in prediction technology.It is a theory that takes the system with incomplete information as the research object and uses specific methods to describe the system with incomplete information and to forecast,make decisions and control it.Grey model GM(1,1)is one of the main contents of grey theory system.It is a time series prediction model,which can be modeled and predicted according to a small amount of information.It is widely used in prediction field.For small sample oscillation sequence modeling,the traditional grey prediction model can only describe and predict the general trend of system behavior sequence change,but it can not recognize the oscillation characteristics in the original sequence and make effective prediction.Therefore,it is of far-reaching significance to further improve the prediction accuracy of the grey prediction model and expand its scope of application,so that it can make more accurate prediction of small sample oscillation sequence.This paper mainly improves the traditional GM(1,1)model and obtains four optimization models:the optimal dimension GM(1,1)model,the GM(1,1)power exponential optimization model,the grey interval GM(1,1)model?and the grey interval GM(1,1)model?.Four optimization models and the traditional GM(1,1)model are compared by empirical analysis in modeling and prediction accuracy of small sample oscillation sequence.The main contents of this paper are as follows:Firstly,the optimal dimension GM(1,1)model is constructed.The optimal dimension of GM(1,1)model is determined by two parameters in the posterior error test of GM(1,1)model,i.e.small residual probability p and variance ratio C.The prediction accuracy of the optimal dimension GM(1,1)model is studied by empirical analysis.Secondly,the GM(1,1)power exponential optimization model is constructed.Taking the minimum cumulative prediction error as the objective function,the optimal power exponent is obtained.The prediction accuracy of GM(1,1)power exponential optimization model is studied by empirical analysis.Thirdly,the grey interval GM(1,1)model?and the grey interval GM(1,1)model?are constructed.The prediction method is extended from point prediction to interval prediction.The two interval prediction methods adopt different upper and lower bound sequence partition methods and different interval weighting methods respectively.The prediction accuracy of grey interval GM(1,1)model is studied by empirical analysis.Finally,based on the improved model,the grey interval GM(1,1)model?and the grey interval GM(1,1)model?are constructed by the data of the Shanghai stock housing transaction area series from 2001 to 2017,and the data of Shanghai stock housing transaction area from 2018 to 2022 is predicted.The results show that the optimal dimension GM(1,1)model and the GM(1,1)power exponential optimization model can not improve the prediction accuracy of small sample oscillation series,and the two grey interval GM(1,1)models can significantly improve the prediction accuracy of small sample oscillation series.Finally,based on the series data of Shanghai stock housing transaction area from 2001 to 2017,the two grey interval GM(1,1)models are selected to forecast the data of Shanghai stock housing transaction area from2018 to 2022,the data will change in a specific range.It can provide a reliable quantitative basis for the government to control the real estate market price.