Efficient Estimation of Integrated Volatility Functionals via Multiscale Jackknife

31 Pages Posted: 28 Mar 2017 Last revised: 18 Apr 2018

See all articles by Jia Li

Jia Li

Duke University

Yunxiao Liu

University of North Carolina (UNC) at Chapel Hill

Dacheng Xiu

University of Chicago - Booth School of Business

Date Written: March 27, 2017

Abstract

We propose semi-parametrically efficient estimators for general integrated volatility functionals of multivariate semimartingale processes. It is known that a plug-in method that uses nonparametric estimates of spot volatilities induces high-order biases which 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, semi-parametrically 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 very convenient to implement.

Suggested Citation

Li, Jia and Liu, Yunxiao and Xiu, Dacheng, Efficient Estimation of Integrated Volatility Functionals via Multiscale Jackknife (March 27, 2017). Chicago Booth Research Paper No. 17-05. Available at SSRN: https://ssrn.com/abstract=2942235 or http://dx.doi.org/10.2139/ssrn.2942235

Jia Li

Duke University ( email )

100 Fuqua Drive
Durham, NC 27708-0204
United States

Yunxiao Liu

University of North Carolina (UNC) at Chapel Hill ( email )

102 Ridge Road
Chapel Hill, NC NC 27514
United States

Dacheng Xiu (Contact Author)

University of Chicago - Booth School of Business ( email )

5807 S. Woodlawn Avenue
Chicago, IL 60637
United States

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