Research On Prediction Model Based On Barycentric Rational Interpolation Function

The prediction is based on historical and present information,and uses scientific methods to judge the future development.As the premise of scientific decision-making,prediction has received extensive attention from the academic circle for a long time.It has important theoretical and practical value in the fields of economy,management,information technology,energy and environment and so on.The nature of predictive modeling can be largely attributed to problems of function approximation and curve fitting.Although the traditional approximation methods such as polynomial and spline have achieved fruitful results in the prediction research,but still need to constantly develop new predictive methods,in order to adapt to the increasingly complex and diverse data environment.As a kind of important approximation tools,the main research work of the barycentric rational interpolation function concentrates on the theoretical properties,but applications of the function need to be further explored.Froma new point of view,this paper studies the traditional prediction theory and methods based on the barycentric rational interpolation function,so as to provide a new approach for predictive modeling and a new method for scientific decision-making.We selected "Research on prediction model based on the barycentric rational interpolation function" as the topic of this paper through integrating the discipline of management,computational mathematics,economics and statistics,And combining theoretical analysis and experiment study,we detail the research as:Firstly,we aim to study the barycentric rational interpolation function theoretically,and prove its superiority in convergence and other aspects;thus it provide a solid theoretical foundation for prediction modeling.Secondly,we choose the main research objects as follows:support vector machine(SVM)model in pattern recognition,nonparametric regression model and semi-parametric regression model in statistical regression,the grey prediction model of "poor information".A new predictive method of these models is constructed based on the barycentric rational interpolation function.The main work and innovations are as follows:(1)We extended the barycentric rational interpolation function theoretically,and it has the following properties:Firstly,it meets the second order derivative interpolation conditions.Secondly,it has no real poles on any real interval.Thirdly,it has arbitrarily high approximation orders on any real interval,regardless of the distribution of points.Fourthly,it can be written as the barycentric form.Finally,numerical results also show that the convergence orders of the new interpolation function is three units larger than tradition barycentric rational interpolation and cubic spline function at every differentiation.(2)Based on the barycentric rational interpolation function,we propose a new kernel function(BRI)for SVM from perspective of function approximation and nature of kernel function,which has better learning and generalization ability theoretically.Numerical results show that the new model not only has better performance in classification,but also improves the dependence of traditional kernel functions on the distribution of data.(3)Based on the barycentric rational interpolation function,we propose a new prediction model for nonparametric regression,which include construction of basis function,parameter estimation and test,knot selection and model prediction.Compared with the traditional model based on spline function,it has the following advantages.Firstly,it has higher smoothness in fitting curve.Secondly,it has lower computational complexity in estimating parameter.Thirdly,it has richer significance of estimation parameters.Our empirical result are based on the term structure of treasury bills in Shanghai Stock Exchange,and the results show that the new model not only has better performance in structure analysis,computational complexity,prediction capability and economic significance,but also improve the fitting and pricing the accuracy of bond.(4)Based on the barycentric rational interpolation function,a new prediction model for semi-parametric regression is proposed.A set of modeling methodology,includes mathematical expression,parameter estimation and test,model selection and prediction,is studied in detail.Compared with the traditional model based on spline function,the new model has the following advantages.Firstly,it has higher smoothness and definite analytic expression in fitting curve.Secondly,under the same node,it has less parameter and richer significance in estimating parameter.Finally,the new model was applied to study on Phillips curve in China in order to make predictions on the inflation rate,and the results show that it not only fully explores the nonlinear characteristics of Phillips curve in China,but also improves the accuracy of inflation prediction effectively.(5)For grey prediction modeling,firstly,we deal with the morbidity of GM(1,1)model by using multiply transformation and orthogonal transformation respectively.Secondly,based on the barycentric rational interpolation function,we propose a new GM(1,1)model;its main advantage lies in improving the reconstruction quality of background value;optimizing initial conditions and parameters.Finally,based on the vector-valued barycentric rational interpolation function,we propose a new method for constructing the background value of MGM(l,m)model,which reduce the computational complexity and improved the predictive performance.The experimental results show that the above methods can improve the stability,applicability and prediction accuracy of grey prediction models.This paper expands the research area of traditional prediction model,enriches the modeling methodologies for traditional prediction model.It has important theoretical and practical value to improve the modeling efficiency of the traditional prediction model.