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Kernel Estimation of Spot Volatility with Microstructure Noise Using Pre-Averaging

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  • Jos'e E. Figueroa-L'opez
  • Bei Wu

Abstract

We first revisit the problem of estimating the spot volatility of an It\^o semimartingale using a kernel estimator. We prove a Central Limit Theorem with optimal convergence rate for a general two-sided kernel. Next, we introduce a new pre-averaging/kernel estimator for spot volatility to handle the microstructure noise of ultra high-frequency observations. We prove a Central Limit Theorem for the estimation error with an optimal rate and study the optimal selection of the bandwidth and kernel functions. We show that the pre-averaging/kernel estimator's asymptotic variance is minimal for exponential kernels, hence, justifying the need of working with kernels of unbounded support as proposed in this work. We also develop a feasible implementation of the proposed estimators with optimal bandwidth. Monte Carlo experiments confirm the superior performance of the devised method.

Suggested Citation

  • Jos'e E. Figueroa-L'opez & Bei Wu, 2020. "Kernel Estimation of Spot Volatility with Microstructure Noise Using Pre-Averaging," Papers 2004.01865, arXiv.org, revised Feb 2022.
    • Handle: RePEc:arx:papers:2004.01865
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    References listed on IDEAS

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    1. Ole E. Barndorff-Nielsen & Peter Reinhard Hansen & Asger Lunde & Neil Shephard, 2008. "Designing Realized Kernels to Measure the ex post Variation of Equity Prices in the Presence of Noise," Econometrica, Econometric Society, vol. 76(6), pages 1481-1536, November.
    2. Richard Y. Chen, 2018. "Inference for Volatility Functionals of Multivariate It\^o Semimartingales Observed with Jump and Noise," Papers 1810.04725, arXiv.org, revised Nov 2019.
    3. Yacine Aït-Sahalia & Jean Jacod, 2014. "High-Frequency Financial Econometrics," Economics Books, Princeton University Press, edition 1, number 10261.
    4. Yacine Aït-Sahalia & Dacheng Xiu, 2019. "Principal Component Analysis of High-Frequency Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 114(525), pages 287-303, January.
    5. Alexander Alvarez & Fabien Panloup & Monique Pontier & Nicolas Savy, 2012. "Estimation of the instantaneous volatility," Statistical Inference for Stochastic Processes, Springer, vol. 15(1), pages 27-59, April.
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    Cited by:

    1. Maria Elvira Mancino & Tommaso Mariotti & Giacomo Toscano, 2022. "Asymptotic Normality for the Fourier spot volatility estimator in the presence of microstructure noise," Papers 2209.08967, arXiv.org.
    2. B. Cooper Boniece & Jos'e E. Figueroa-L'opez & Yuchen Han, 2023. "Data-driven fixed-point tuning for truncated realized variations," Papers 2311.00905, arXiv.org, revised Oct 2024.

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