Parameter Estimation Of Ornstein-Uhlenbeck Process

Ornstein-Uhlenbeck process is one kind of diffusion processes,which is widely used in physics and finance. In this paper,I estimate the parameter of it based on the theory of estimating functions via parameter transformation,using a simple and explicit estimating function to estimate one part of the parameter first,and then using the optimal quadratic martingale estimating function for the remaining part of the parameter. Comparing with the maximum likelihood estimator, the new estimator obtaining from this method not only has simple form and need not much computation,but also has good asymptotic properties. In the end,I compare this estimator with estimators obtained by maximum likelihood and Euler approximation method via Monte Carlo numerical simulation.The paper is of four parts.Chapter one is the introduction.Section one of Chapter two introduces the mathematical model of Ornstein-Uhlenbeck process,and explains the physical meaning of the process as well as its parameters.Section two recalls some related basic knowledge and displays some definitions ,suppo-sitions and theories involved in the paper. Chaper three is the main body of the paper.Section one describes the estimator of the process obtained by Euler approximation method,Section two describes the maximum-likelihood estimator,and Section three describes the estimator of the process based on estimating function theories.Chapter four illustrates the comparison results of Monte Carlo simulation.Finally,some concluding remarks and expectations of my work are given.