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February 2019 Efficient estimation of integrated volatility functionals via multiscale jackknife
Jia Li, Yunxiao Liu, Dacheng Xiu
Ann. Statist. 47(1): 156-176 (February 2019). DOI: 10.1214/18-AOS1684


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.


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Jia Li. Yunxiao Liu. Dacheng Xiu. "Efficient estimation of integrated volatility functionals via multiscale jackknife." Ann. Statist. 47 (1) 156 - 176, February 2019.


Received: 1 March 2017; Revised: 1 September 2017; Published: February 2019
First available in Project Euclid: 30 November 2018

zbMATH: 07036198
MathSciNet: MR3909930
Digital Object Identifier: 10.1214/18-AOS1684

Primary: 60F05, 60G44, 62F12

Rights: Copyright © 2019 Institute of Mathematical Statistics


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Vol.47 • No. 1 • February 2019
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