基于离散观测下Cauchy-OU过程的最大似然估计

Maximum Likelihood Estimation of Discretely SampledCauchy-OU Processes

基于离散观测样本,本文研究Cauchy-OU过程的参数估计问题.在大多数情况下,离散时间的最大似然函数是不能直接计算出来的,因此采用傅里叶变换及Gaver-Stehfest算法,构造似然函数的一个显式逼近序列,且该序列收敛于真实(但未知)的似然函数.最后,采用最大似然估计法估计出未知参数.仿真实验表明,所得到的参数估计是比较准确且稳定的.

Based on discrete observation samples,this paper studies the parameter estimation problem of Cauchy-OU processes.In most cases,the maximum likelihood function in discrete time can’t be calculated directly,therefore,in this paper we use the Fourier transform and Gaver-Stehfest algorithm,constructing an explicit approximation sequence of likelihood function,which converges to the real(but unknown)likelihood function.Finally,the maximum likelihood estimation method is used to estimate the unknown parameters.Experiments in the simulations show that the proposed estimation method is more accurate and stable.