Interval Number Series Prediction Based On Several Grey Regression Models

Grey model is mainly used to predict the exact number series.However,there are many data with dynamic volatility in complicated uncertain systems.And when they are expressed as interval numbers,the growth trend and the range of change can be reflected more obviously.If the grey models are suitable for the interval number series,more practical problems can be solved.Therefore,an in-depth study is carried out on improving models,extending modeling object,optimizing the lag order of interval number series,etc.The main research contents are as following.(1)The time-delay effect is pervasive in uncertain systems.Considering its impact on the system characteristics,an auto-regressive GM(1,N)is constructed based on GM(1,N)by introducing the auto-regressive terms of the system characteristics and the grey action.Furthermore,the variables of the model are regarded as column vectors,and the parameters are set as matrix form.Then,a matrix auto-regression GM(1,N)is established,which is suitable for the interval number series with time delay.On the basis of the model,a new technique is presented for determining the optimal lag order of interval number series,which can improve the fitting and prediction accuracy of the model.(2)The time-delay effect is not only reflected in the influence of system characteristics on its own development,but also in the delay of the action and result among various factors.Therefore,the delay regression terms of the system characteristics and its related factors are introduced into the traditional grey model.Then,a matrix grey multi-variable model with time-delay is proposed by changing the model into matrix form and combining with the new technique for determining the optimal lag order.Thus,the simulation effect of the model is optimized effectively.(3)GM(1,1)is applicable to the series with exponential growth and small fluctuation,but it is not accurate to predict the series with parabolic or saturated development trends.So the traditional GM(1,1)is coupled with the quadratic polynomial model and converted it into matrix form,which enhances the compatibility of the model and enriches the types of applicable series.The parameters of the models are estimated by the least square method,and the prediction formulas of the models are given.In the modeling and forecasting,the integrity of the interval numbers are maintained and the relations between the boundaries are considered,so that the models can be applied to the interval number series directly.Finally,the new models are used in the fields of economics and transportation.By comparing with quadratic polynomial model,GM(1,1),GM(1,N),MBIGM(1,1),MINGM(1,N)and other competitive models,the effectiveness and superiority of the new models are verified.