Volatility estimators for discretely sampled Levy processes

• 成果类型: Article
• 署名作者: Ait-Sahalia, Yacine; Jacod, Jean
• 署名单位: Princeton University; National Bureau of Economic Research; Sorbonne Universite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris Cite
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/009053606000001190
• 发表日期: 2007
• 页码: 355-392
• 关键词: STATISTICAL-INFERENCE; stable-distributions; parameters; models

摘要

This paper studies the estimation of the volatility parameter in a model where the driving process is a Brownian motion or a more general symmetric stable process that is perturbed by another Levy process. We distinguish between a parametric case, where the law of the perturbing process is known, and a semiparametric case, where it is not. In the parametric case, we construct estimators which are asymptotically efficient. In the semiparametric case, we can obtain asymptotically efficient estimators by sampling at a sufficiently high frequency, and these estimators are efficient uniformly in the law of the perturbing process.