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August 2013 Volatility occupation times
Jia Li, Viktor Todorov, George Tauchen
Ann. Statist. 41(4): 1865-1891 (August 2013). DOI: 10.1214/13-AOS1135

Abstract

We propose nonparametric estimators of the occupation measure and the occupation density of the diffusion coefficient (stochastic volatility) of a discretely observed Itô semimartingale on a fixed interval when the mesh of the observation grid shrinks to zero asymptotically. In a first step we estimate the volatility locally over blocks of shrinking length, and then in a second step we use these estimates to construct a sample analogue of the volatility occupation time and a kernel-based estimator of its density. We prove the consistency of our estimators and further derive bounds for their rates of convergence. We use these results to estimate nonparametrically the quantiles associated with the volatility occupation measure.

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Jia Li. Viktor Todorov. George Tauchen. "Volatility occupation times." Ann. Statist. 41 (4) 1865 - 1891, August 2013. https://doi.org/10.1214/13-AOS1135

Information

Published: August 2013
First available in Project Euclid: 5 September 2013

zbMATH: 1277.62196
MathSciNet: MR3127851
Digital Object Identifier: 10.1214/13-AOS1135

Subjects:
Primary: 62F12 , 62M05
Secondary: 60H10 , 60J75

Keywords: high-frequency data , local approximation , nonparametric estimation , occupation time , quantiles , spot variance , stochastic volatility

Rights: Copyright © 2013 Institute of Mathematical Statistics

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Vol.41 • No. 4 • August 2013
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