α-stable运动驱动的OU过程的拟似然估计

方龙祥, 张新生

数学学报 ›› 2014, Vol. 57 ›› Issue (2) : 395-408.

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数学学报 ›› 2014, Vol. 57 ›› Issue (2) : 395-408. DOI: 10.12386/A2014sxxb0039
论文

α-stable运动驱动的OU过程的拟似然估计

    方龙祥1, 张新生2
作者信息 +

Quasi-Likelihood Estimation for OU Processes Driven by α-Stable Motions

    Long Xiang FANG1, Xin Sheng ZHANG2
Author information +
文章历史 +

摘要

对于α-stable 运动驱动的OU过程，其转移密度函数没有明确的显式表达式，但是条件特征函数已知.本文基于离散观测样本，借助条件特征函数，研究了α-stable运动驱动的OU过程的拟似然估计，并证明了拟似然估计量的相合性和渐近有效性.模拟显示所提出的估计方法是准确和稳定的.

Abstract

For OU processes driven by α-stable motions, its transition density function has no explicit form, while the conditional characteristic function is known. In this paper, we present an quasi-likelihood estimation procedure for parameters of the discretely sampled process of OU processes driven by α-stable motions. The proposed procedure is based on the conditional characteristic function, and the quasi-likelihood estimator is proved to be consistent and asymptotically efficient under some mild conditions. Finally, Monte Carlo simulations are conducted to demonstrate the accuracy and stability of proposed estimator.

关键词

α-stable运动驱动的OU过程 / 条件特征函数 / 拟似然估计 / Fisher信息阵

Key words

OU processes driven by α-stable motions / conditional characteristic function / quasi-likelihood estimation / Fisher information matrix

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方龙祥, 张新生. α-stable运动驱动的OU过程的拟似然估计. 数学学报, 2014, 57(2): 395-408 https://doi.org/10.12386/A2014sxxb0039
Long Xiang FANG, Xin Sheng ZHANG. Quasi-Likelihood Estimation for OU Processes Driven by α-Stable Motions. Acta Mathematica Sinica, Chinese Series, 2014, 57(2): 395-408 https://doi.org/10.12386/A2014sxxb0039

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基金

国家自然科学基金资助项目（11071045，11201003）；安徽省自然科学基金（1408085MA07，1208085MA11）及高校省级重点科学研究项目（KJ2013A137）
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