Estimators of diffusions with randomly spaced discrete observations: A general theory

• 成果类型: Article
• 署名作者: Aït-Sahalia, Y; Mykland, PA
• 署名单位: Princeton University; National Bureau of Economic Research; University of Chicago
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/009053604000000427
• 发表日期: 2004
• 页码: 2186-2222
• 关键词: maximum-likelihood-estimation

摘要

We provide a general method to analyze the asymptotic properties of a variety of estimators of continuous time diffusion processes when the data are not only discretely sampled in time but the time separating successive observations may possibly be random. We introduce a new operator, the generalized infinitesimal generator, to obtain Taylor expansions of the asymptotic moments of the estimators. As a special case, our results apply to the situation where the data are discretely sampled at a fixed nonrandom time interval. We include as specific examples estimators based on maximum-likelihood and discrete approximations such as the Euler scheme.