ON THE APPROXIMATE MAXIMUM LIKELIHOOD ESTIMATION FOR DIFFUSION PROCESSES

• 成果类型: Article
• 署名作者: Chang, Jinyuan; Chen, Song Xi
• 署名单位: Peking University; Peking University; Iowa State University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/11-AOS922
• 发表日期: 2011
• 页码: 2820-2851
• 关键词: closed-form approximation; discrete observations; term structure; high-frequency; models

摘要

The transition density of a diffusion process does not admit an explicit expression in general, which prevents the full maximum likelihood estimation (MLE) based on discretely observed sample paths. Ait-Sahalia [J. Finance 54 (1999) 1361-1395; Econometrica 70 (2002) 223-262] proposed asymptotic expansions to the transition densities of diffusion processes, which lead to an approximate maximum likelihood estimation (AMLE) for parameters. Built on Ait-Sahalia's [Econometrica 70 (2002) 223-262; Ann. Statist. 36 (2008) 906-937] proposal and analysis on the AMLE, we establish the consistency and convergence rate of the AMLE, which reveal the roles played by the number of terms used in the asymptotic density expansions and the sampling interval between successive observations. We find conditions under which the AMLE has the same asymptotic distribution as that of the full MLE. A first order approximation to the Fisher information matrix is proposed.