The GM(1,1) Model Construction And Application Considering The Characteristics Of Periodic Fluctuation Data

There are many uncertain things in real life,people need to be prepared for the future events and various situations,that is “plan ahead”.People need to predict the future development of events,that is,to predict what will happen or forecast the outcome for better economic production and other activities.However,due to the fact that it is difficult to obtain the real data and the asymmetry of the information,the amount of the effective information is small,which brings some difficulties to the actual prediction.In order to make an accurate prediction of the actual situation,we must solve the problem through reasonable methods.Since the theory of grey system was put forward,it has been accepted by many scholars because it needs less data and can deal with poor information.Existing grey prediction models,such as mean value GM(1,1)model,grey Verhulst model,GM(1,1)power model and non-equidistant model,have been proved to be feasible and practical by practice,and have been widely used in engineering applications,energy prediction,the grain forecast and the emerging industry forecast,it provides a good solution for people to solve the actual forecast problem.However,the traditional grey prediction model has some limitations--the traditional GM(1,1)is only suitable to deal with the time series with obvious increasing trend.But the time series not only has the growth tendency,but also has the periodic characteristic,the lag characteristic as well as the stochastic fluctuation and so on.Therefore,the traditional grey prediction model has no advantage for the time series forecasting problem with both fluctuation and growth trend.To solve the problem that the traditional GM(1,1)model can not deal with the time series prediction with periodic fluctuation,this paper proposes a new grey prediction model based on the traditional GM(1,1)model.This paper analyzed and processed the data with the characteristics of periodic fluctuation,construct a new grey prediction model,and use it in practice to verify the validity of the model.In this paper,the quarterly periodic GM(1,1)model GM(1,1)-Fourier model is constructed respectively to analyze the time series data with periodic fluctuation characteristics from the perspectives of improved seasonal index and data separation modeling and reorganization.For the quarterly periodic GM(1,1)model,this paper analyzes the deficiency of the calculation method of seasonal index in the traditional grey seasonal model,and adopts the new method to calculate the seasonal index,at the same time,a new quarterly periodic GM(1,1)model is constructed by GM(1,1)model as trend term to solve the time series forecasting problem.For the GM(1,1)-Fourier model,the periodic fluctuation term and the trend growth term are separated for the time series with both the growth trend and the periodic fluctuation.The trend growth term is modeled by GM(1,1)model,the periodic wave term is modeled by Fourier series,and then the parts of the model are added to construct GM(1,1)Fourier model to further predict the time series.The method of dealing with the time series with the characteristics of periodic fluctuation is analyzed from two different angles,and it is considered to be applied to the prediction of railway passenger volume.The forecasting results of the two models are compared with those of the traditional GM(1,1),SGM(1,1),ARIMA model,Holt-Winters model,exponential smoothing method and moving average models,and analyzed the advantages and disadvantages of each model.For the fitting and forecasting results of railway passenger volume,it can be seen that the model proposed in this paper has significant advantages in predicting and fitting.It can be used to forecast the actual railway passenger volume and provide reference for the reasonable planning of railway departments.