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

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 han...

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Bibliographic Details
Published in:Econometric theory 2024-06, Vol.40 (3), p.558-607
Main Authors: Figueroa-López, José E., Wu, Bei
Format: Article
Language:English
Subjects:
Approximation
Bandwidths
Central limit theorem
Convergence
Econometrics
Economic theory
Noise
Portfolio management
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Summary: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.
ISSN:0266-4666
1469-4360
DOI:10.1017/S0266466622000470