Publication Type
Journal Article
Version
publishedVersion
Publication Date
2-2019
Abstract
We propose semiparametrically efficient estimators for general integrated volatility functionals of multivariate semimartingale processes. A plug-in method that uses nonparametric estimates of spot volatilities is known to induce high-order biases that need to be corrected to obey a central limit theorem. Such bias terms arise from boundary effects, the diffusive and jump movements of stochastic volatility and the sampling error from the nonparametric spot volatility estimation. We propose a novel jackknife method for bias correction. The jackknife estimator is simply formed as a linear combination of a few uncorrected estimators associated with different local window sizes used in the estimation of spot volatility. We show theoretically that our estimator is asymptotically mixed Gaussian, semiparametrically efficient, and more robust to the choice of local windows. To facilitate the practical use, we introduce a simulation-based estimator of the asymptotic variance, so that our inference is derivative-free, and hence is convenient to implement.
Keywords
high-frequency data, jackknife, Semimartingale, spot volatility
Discipline
Econometrics
Research Areas
Econometrics
Publication
Annals of Statistics
Volume
47
Issue
1
First Page
156
Last Page
176
ISSN
0090-5364
Identifier
10.1214/18-AOS1684
Publisher
Institute of Mathematical Statistics (IMS)
Citation
LI, Jia; LIU, Yunxiao; and XIU, Dacheng..
Efficient estimation of integrated volatility functionals via multi-scale jackknife. (2019). Annals of Statistics. 47, (1), 156-176.
Available at: https://ink.library.smu.edu.sg/soe_research/2585
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/10.1214/18-AOS1684