A REMARK ON THE RATES OF CONVERGENCE FOR INTEGRATED VOLATILITY ESTIMATION IN THE PRESENCE OF JUMPS
成果类型：
Article
署名作者：
Jacod, Jean; Reiss, Markus
署名单位：
Universite Paris Cite; Sorbonne Universite; Humboldt University of Berlin
刊物名称：
ANNALS OF STATISTICS
ISSN/ISSBN：
0090-5364
DOI：
10.1214/13-AOS1179
发表日期：
2014
页码：
1131-1144
关键词：
摘要：
The optimal rate of convergence of estimators of the integrated volatility, for a discontinuous Ito semimartingale sampled at regularly spaced times and over a fixed time interval, has been a long-standing problem, at least when the jumps are not summable In this paper, we study this optimal rate, in the minimax sense and for appropriate bounded nonparametric classes of semimartingales. We show that, if the rth powers of the jumps are sununable for some r is an element of [0, 2), the minimax rate is equal to min(root 2, (n log n)((2-r)/2)), where n is the number of observations.
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