Research And Application On Time Series Forecasting Algorithm Based On Hausdorff Fractional Grey Model

Time series exist in people’s social production activities,but there are complex factors behind the data presented by many time series.Grey model have good predictive performance in uncertain systems,so it is very suitable to use grey model to forecast time series affected by complex factors.The fractional extension is an important research direction of the grey model.The fractional accumulative grey model(FAGM(1,1))is the first to introduce the concept of fractional order.However,there is a factorial operator in the accumulation matrix in the FAGM(1,1),which makes the calculation overflow in the calculation of the elements in the accumulation matrix.Aiming at the problems existing in the FAGM(1,1),this thesis firstly uses the Hausdorff fractional derivative to re-derive the accumulated matrix in the model and solves the problem of the calculation overflow of matrix elements.Then,the background value of the FAGM(1,1)is optimized by the Newton-Cortes formula,which reduces the calculation error of the model.Combined with the above improvements,this thesis proposes a Hausdorff fractional accumulative grey model(HFAGM(1,1))suitable for one-dimensional time series forecasting problems.The fractional grey model with convolution(FGMC(1,m))is a high-dimensional extension based on the FAGM(1,1),so the FGMC(1,m)also has the same problems as the FAGM(1,1).In this thesis,the method of improving the FAGM(1,1)is extended to the FGMC(1,m),and a Hausdorff fractional grey convolution model(HFGMC(1,m))is proposed for high-dimensional time series forecasting problems.In the experimental analysis,HFAGM(1,1)is applied to the consumption prediction of coalbed methane and LNG.The experimental results show that the Hausdorff fractional derivative and the Newton-Cotes formula can improve the prediction performance of the FAGM(1,1).The HFGMC(1,m),which is suitable for multi-dimensional time series,will be applied to the time series of stock prices.The experimental results show that the HFGMC(1,m)has excellent predictive performance.Finally,the HFGMC(1,m)is combined with the BP neural network to obtain a hybrid model,which enhances the nonlinear fitting ability of the HFGMC(1,m).The experimental results show that the prediction performance of the HFGMC(1,m)with enhanced nonlinear fitting ability has been effectively improved.