Publication Type

Journal Article

Version

publishedVersion

Publication Date

8-2013

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.

Keywords

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

Discipline

Econometrics | Economic Theory

Research Areas

Econometrics

Publication

Annals of Statistics

Volume

41

Issue

4

First Page

1865

Last Page

1891

ISSN

0090-5364

Identifier

10.1214/13-AOS1135

Publisher

Institute of Mathematical Statistics (IMS)

Copyright Owner and License

Publisher

Additional URL

https://doi.org/10.1214/13-AOS1135

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