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Estimation of Integrated Volatility Functionals with Kernel Spot Volatility Estimators

José E. Figueroa-López, Jincheng Pang, Bei Wu

arXiv 13 Jul 2024 · Econometrics · publishedEconometric Theory (2025)

arXiv:2407.09759 · PDF · DOI · OpenAlex · Extracted main text

Abstract

For a multidimensional It\^o semimartingale, we consider the problem of estimating integrated volatility functionals. Jacod and Rosenbaum (2013) studied a plug-in type of estimator based on a Riemann sum approximation of the integrated functional and a spot volatility estimator with a forward uniform kernel. Motivated by recent results that show that spot volatility estimators with general two-side kernels of unbounded support are more accurate, in this paper, an estimator using a general kernel spot volatility estimator as the plug-in is considered. A biased central limit theorem for estimating the integrated functional is established with an optimal convergence rate. Unbiased central limit theorems for estimators with proper de-biasing terms are also obtained both at the optimal convergence regime for the bandwidth and when applying undersmoothing. Our results show that one can significantly reduce the estimator's bias by adopting a general kernel instead of the standard uniform kernel. Our proposed bias-corrected estimators are found to maintain remarkable robustness against bandwidth selection in a variety of sampling frequencies and functions.

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19
references
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distinct cited
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Most heavily cited references

The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.

ReferenceIntensityMentionsSectionsMain text
1Jacod, J. & Rosenbaum, M (2013) Quarticity and other functionals of volatility: efficient estimation0.94112483%
2Figueroa-López, J. E. & Li, C (2020) Optimal kernel estimation of spot volatility of stochastic differential equations self0.92810580%
3Li, J., Liu, Y., Xiu, D. et al (2019) Efficient estimation of integrated volatility functionals via multiscale jackknife0.874102100%
4Kristensen, D (2010) Nonparametric filtering of the realized spot volatility: A kernel-based approach0.87472100%
5Jacod, J. & Rosenbaum, M (2015) Estimation of volatility functionals: The case of a $n$ window0.85221562%
6Figueroa-López, J. E. & Wu, B (2024) Kernel estimation of spot volatility with microstructure noise using pre-averaging self0.8434375%
7Fan, J. & Wang, Y (2008) Spot volatility estimation for high-frequency data0.73732100%
8Jacod, J. & Protter, P (2011) Discretization of processes0.58510230%
9Aït-Sahalia, Y. & Jacod, J (2014) High-frequency financial econometrics0.5112250%
10Renault, E., Sarisoy, C. & Werker, B (2017) Efficient estimation of integrated volatility and related processes0.51121100%

Showing the top 10 of 19 scored citations.