QUARTICITY AND OTHER FUNCTIONALS OF VOLATILITY: EFFICIENT ESTIMATION
成果类型：
Article
署名作者：
Jacod, Jean; Rosenbaum, Mathieu
署名单位：
Sorbonne Universite; Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Centre National de la Recherche Scientifique (CNRS); Sorbonne Universite
刊物名称：
ANNALS OF STATISTICS
ISSN/ISSBN：
0090-5364
DOI：
10.1214/13-AOS1115
发表日期：
2013
页码：
1462-1484
关键词：
摘要：
We consider a multidimensional Ito semimartingale regularly sampled on [0, t] at high frequency 1/Delta(n), with Delta(n) going to zero. The goal of this paper is to provide an estimator for the integral over [0, t] of a given function of the volatility matrix. To approximate the integral, we simply use a Riemann sum based on local estimators of the pointwise volatility. We show that although the accuracy of the pointwise estimation is at most Delta(1/4)(n), this procedure reaches the parametric rate Delta(1/2)(n), as it is usually the case in integrated functionals estimation. After a suitable bias correction, we obtain an unbiased central limit theorem for our estimator and show that it is asymptotically efficient within some classes of sub models.
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