MAXIMUM-LIKELIHOOD ESTIMATION FOR DIFFUSION PROCESSES VIA CLOSED-FORM DENSITY EXPANSIONS

• 成果类型: Article
• 署名作者: Li, Chenxu
• 署名单位: Peking University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/13-AOS1118
• 发表日期: 2013
• 页码: 1350-1380
• 关键词: STOCHASTIC DIFFERENTIAL-EQUATIONS; discretely sampled diffusions; CONTINUOUS-TIME MODELS; malliavin calculus; asymptotic expansions; approximation approach; nonlinear diffusions; transition densities; simulated likelihood; wiener functionals

摘要

This paper proposes a widely applicable method of approximate maximum-likelihood estimation for multivariate diffusion process from discretely sampled data. A closed-form asymptotic expansion for transition density is proposed and accompanied by an algorithm containing only basic and explicit calculations for delivering any arbitrary order of the expansion. The likelihood function is thus approximated explicitly and employed in statistical estimation. The performance of our method is demonstrated by Monte Carlo simulations from implementing several examples, which represent a wide range of commonly used diffusion models. The convergence related to the expansion and the estimation method are theoretically justified using the theory of Watanabe [Ann. Probab. 15 (1987) 1-39] and Yoshida [J. Japan Statist. Soc. 22 (1992) 139-159] on analysis of the generalized random variables under some standard sufficient conditions.