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KERNEL ESTIMATION OF SPOT VOLATILITY WITH MICROSTRUCTURE NOISE USING PRE-AVERAGING

Published online by Cambridge University Press:  18 October 2022

José E. Figueroa-López  and
Bei Wu
José E. Figueroa-López*
Affiliation:
Washington University in St. Louis
Bei Wu
Affiliation:
Washington University in St. Louis
*
Address correspondence to José E. Figueroa-López, Department of Mathematics and Statistics, Washington University in St. Louis, St. Louis, MO 63130, USA; e-mail: figueroa-lopez@wustl.edu.
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Abstract

We revisit the problem of estimating the spot volatility of an Itô semimartingale using a kernel estimator. A central limit theorem (CLT) with an optimal convergence rate is established for a general two-sided kernel. A new pre-averaging/kernel estimator for spot volatility is also introduced to handle the microstructure noise of ultra high-frequency observations. A CLT for the estimation error of the new estimator is obtained, and the optimal selection of the bandwidth and kernel function is subsequently studied. It is shown that the pre-averaging/kernel estimator’s asymptotic variance is minimal for two-sided exponential kernels, hence justifying the need of working with kernels of unbounded support. Feasible implementation of the proposed estimators with optimal bandwidth is developed as well. Monte Carlo experiments confirm the superior performance of the new method.

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Type
ARTICLES
Information
Econometric Theory , Volume 40 , Issue 3 , June 2024 , pp. 558 - 607
Copyright
© The Author(s), 2022. Published by Cambridge University Press

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Footnotes

The authors are truly grateful to the Editor (Dr. Peter Phillips), the Co-Editor (Dr. Dennis Kristensen), and two anonymous referees for their numerous suggestions that helped to significantly improve the original manuscript. The research of the first author was supported in part by the NSF Grants DMS-2015323 and DMS-1613016.

References

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