基于离散观测的次分数Vasicek模型的参数估计  

Parameter estimation for the sub-fractional Vasicek model based on discrete observation

作　　者：张翠芸 郭精军 马爱琴 ZHANG Cuiyun;GUO Jingjun;MA Aiqin(School of Statistics,Lanzhou University of Finance and Economics,Lanzhou 730020,Gansu,China)

机构地区：[1]兰州财经大学统计学院,甘肃兰州730020

出　　处：《山东大学学报（理学版）》2023年第11期15-26,共12页Journal of Shandong University(Natural Science)

基　　金：国家自然科学基金资助项目(71961013);甘肃省教育厅“双一流”科研重点项目(GSSYLXM-06);甘肃省教育厅优秀研究生“创新之星”项目(2021CXZX-701);2021年博士研究生科研创新项目(2021D03)

摘　　要：主要研究由次分数布朗运动驱动的Vasicek模型的统计分析问题。首先,基于离散观测,用最小二乘估计方法给出Vasicek模型中漂移参数μ和θ的估计值;其次,对于θ≠0和θ=0的情况,分别得到估计值的一致性和渐近分布;最后,用Monte Carlo法进行模拟,证明估计值的无偏性和有效性。The problem of statistical analysis of the Vasicek model driven by sub-fractional Brownian motion is mainly investigated.Firstly,based on discrete observations,the estimation of drift parametersμandθin Vasicek model are given by the least square estimation method.Secondly,for theθ≠0 andθ=0 cases,the consistency and the asymptotic distribution of the estimators are obtained,respectively.Finally,simulations are performed with the Monte Carlo method to demonstrate the unbiasedness and validity of the estimates.

关 键 词：次分数布朗运动 最小二乘估计 VASICEK模型 一致性 渐近分布 

分 类 号：O212.1[理学—概率论与数理统计]