The Annals of Statistics

Volatility occupation times

Jia Li, Viktor Todorov, and George Tauchen

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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.

Article information

Source
Ann. Statist., Volume 41, Number 4 (2013), 1865-1891.

Dates
First available in Project Euclid: 5 September 2013

Permanent link to this document
https://projecteuclid.org/euclid.aos/1378386241

Digital Object Identifier
doi:10.1214/13-AOS1135

Mathematical Reviews number (MathSciNet)
MR3127851

Zentralblatt MATH identifier
1277.62196

Subjects
Primary: 62F12: Asymptotic properties of estimators 62M05: Markov processes: estimation
Secondary: 60H10: Stochastic ordinary differential equations [See also 34F05] 60J75: Jump processes

Keywords
Occupation time local approximation stochastic volatility spot variance quantiles nonparametric estimation high-frequency data

Citation

Li, Jia; Todorov, Viktor; Tauchen, George. Volatility occupation times. Ann. Statist. 41 (2013), no. 4, 1865--1891. doi:10.1214/13-AOS1135. https://projecteuclid.org/euclid.aos/1378386241


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