Efficient estimation of integrated volatility functionals via multi-scale jackknife
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 th...
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sg-smu-ink.soe_research-35842022-10-04T04:39:58Z Efficient estimation of integrated volatility functionals via multi-scale jackknife LI, Jia LIU, Yunxiao XIU, Dacheng. 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. 2019-02-01T08:00:00Z text application/pdf https://ink.library.smu.edu.sg/soe_research/2585 info:doi/10.1214/18-AOS1684 https://ink.library.smu.edu.sg/context/soe_research/article/3584/viewcontent/JACKKNIFE_pvoa.pdf http://creativecommons.org/licenses/by-nc-nd/4.0/ Research Collection School Of Economics eng Institutional Knowledge at Singapore Management University high-frequency data jackknife Semimartingale spot volatility Econometrics |
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high-frequency data jackknife Semimartingale spot volatility Econometrics LI, Jia LIU, Yunxiao XIU, Dacheng. Efficient estimation of integrated volatility functionals via multi-scale jackknife |
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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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LI, Jia LIU, Yunxiao XIU, Dacheng. |
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LI, Jia LIU, Yunxiao XIU, Dacheng. |
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LI, Jia |
title |
Efficient estimation of integrated volatility functionals via multi-scale jackknife |
title_short |
Efficient estimation of integrated volatility functionals via multi-scale jackknife |
title_full |
Efficient estimation of integrated volatility functionals via multi-scale jackknife |
title_fullStr |
Efficient estimation of integrated volatility functionals via multi-scale jackknife |
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Efficient estimation of integrated volatility functionals via multi-scale jackknife |
title_sort |
efficient estimation of integrated volatility functionals via multi-scale jackknife |
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Institutional Knowledge at Singapore Management University |
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2019 |
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https://ink.library.smu.edu.sg/soe_research/2585 https://ink.library.smu.edu.sg/context/soe_research/article/3584/viewcontent/JACKKNIFE_pvoa.pdf |
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1770576097159675904 |