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June 2014 A remark on the rates of convergence for integrated volatility estimation in the presence of jumps
Jean Jacod, Markus Reiss
Ann. Statist. 42(3): 1131-1144 (June 2014). DOI: 10.1214/13-AOS1179

Abstract

The optimal rate of convergence of estimators of the integrated volatility, for a discontinuous Itô 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 $r$th powers of the jumps are summable for some $r\in[0,2)$, the minimax rate is equal to $\min(\sqrt{n},(n\log n)^{(2-r)/2})$, where $n$ is the number of observations.

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Jean Jacod. Markus Reiss. "A remark on the rates of convergence for integrated volatility estimation in the presence of jumps." Ann. Statist. 42 (3) 1131 - 1144, June 2014. https://doi.org/10.1214/13-AOS1179

Information

Published: June 2014
First available in Project Euclid: 20 June 2014

zbMATH: 1305.62036
MathSciNet: MR3224283
Digital Object Identifier: 10.1214/13-AOS1179

Subjects:
Primary: 62C20, 62G20, 62M09
Secondary: 60H99, 60J75

Rights: Copyright © 2014 Institute of Mathematical Statistics

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Vol.42 • No. 3 • June 2014
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