Diffusion Process To Transfer Density Estimates

In practice, many systems can be attributed to the diffusion process. the transfer density of Diffusion process has a very important role for the calculation of an important basis characteristics for dynamic and the estimation of the model. so far, Many scholars has been studied the transfer density of Diffusion process, However, these studies are basically limited to the field of the parameter estimation. the Parameter estimation method Is generally assumed some parameters form of model the coefficients, and then estimate the unknown model parameters. because the coefficient concreted can't meet the process variables of the basic dynamics.And may result errors from the outcome of using these models;Unlike the parametric methods, the Non-parametric estimation methods in the data generation process requires less priori information, Assumption of conditions in the overall distribution is wide, Thus the constructed non-parametric statistical method has a good adaptive. when the assumption of the overall distribution is improper, it won't produce Significant errors.Therefore, it has better robustness. for these reasons above, Looking for a non-parametric estimation to estimate the transfer density of Diffusion process is very important.This article Based on the observations of discrete samples, the author make further research on estimating transfer density of the diffusion process, the main work is as follows:Firstly, The paper reviews the present research situation of transfer density of the diffusion process in parameter and non-parametric field, summarized the advantages and limitations of varieties of estimation methods. The paper apply weight adjustment estimation method to estimating transition density, we introduce probability weight factorτ,(x), and useτi(x) to redefine weight function of NW Kernel Estimation, we named this new method Quasi-NW estimation method. Quasi-RNW estimation combine the NW Kernel Estimation and Local Polynominal Estimation together. Possesses good sampling characteristics as Local Polynominal Estimation and the estimator is also non-negative. This paper gives a detailed introduction to the construction and Gradualness of estimator. In addition, we introduced two kinds of bandwidth select method, based on numerical simulation result, the most appropriate bandwidth is selected out for non-parametric estimation of transfer density.Secondly, Based on earlier research, we apply those transfer density estimation methods to estimating the transfer density of two classical diffusion process—CIR Model and Vasicek Model. MATLAB Simulation, residual Comparison and statistics analysis result indicate that non-parametric Quasi-RNW estimation method is better than hermit and Kernel Estimation. We also make use of numerical maximization method to Compare the parameter identification ability of these three estimation methods, the results show that all these three methods can be effectively identify the parameters of Models, but the Quasi-RNW Estimation is best of all, Hermit Estimation is secondly and Kernel Estimation is the worst.Finally, we apply the proposed Quasi-RNW Estimation to analysis the rate of return of shanghai stock index in a period of time, Using the estimated transfer density to predict the fluctuation range of stock index, the predict data compare to the actual data indicate the proposed Quasi-RNW Estimation is very effective, it can be used to provide investment decision-making for investors.