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)
Citation
LI, Jia; TODOROV, Viktor; and TAUCHEN, George.
Volatility occupation times. (2013). Annals of Statistics. 41, (4), 1865-1891.
Available at: https://ink.library.smu.edu.sg/soe_research/2569
Copyright Owner and License
Publisher
Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial-No Derivative Works 4.0 International License.
Additional URL
https://doi.org/10.1214/13-AOS1135