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NONPARAMETRIC ESTIMATION OF LARGE SPOT VOLATILITY MATRICES FOR HIGH-FREQUENCY FINANCIAL DATA

Published online by Cambridge University Press:  07 April 2025

Ruijun Bu ,
Degui Li ,
Oliver Linton  and
Hanchao Wang
Ruijun Bu
Affiliation:
University of Liverpool
Degui Li
Affiliation:
University of Macau
Oliver Linton*
Affiliation:
University of Cambridge
Hanchao Wang
Affiliation:
Shandong University
*
Address correspondence to Oliver Linton, Faculty of Economics, University of Cambridge, Cambridge, UK; e-mail: [email protected].
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Abstract

In this paper, we consider estimating spot/instantaneous volatility matrices of high-frequency data collected for a large number of assets. We first combine classic nonparametric kernel-based smoothing with a generalized shrinkage technique in the matrix estimation for noise-free data under a uniform sparsity assumption, a natural extension of the approximate sparsity commonly used in the literature. The uniform consistency property is derived for the proposed spot volatility matrix estimator with convergence rates comparable to the optimal minimax one. For high-frequency data contaminated by microstructure noise, we introduce a localized pre-averaging estimation method that reduces the effective magnitude of the noise. We then use the estimation tool developed in the noise-free scenario and derive the uniform convergence rates for the developed spot volatility matrix estimator. We further combine kernel smoothing with the shrinkage technique to estimate the time-varying volatility matrix of the high-dimensional noise vector. In addition, we consider large spot volatility matrix estimation in time-varying factor models with observable risk factors and derive the uniform convergence property. We provide numerical studies including simulation and empirical application to examine the performance of the proposed estimation methods in finite samples.

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ARTICLES
Information
Econometric Theory , First View , pp. 1 - 38
Copyright
© The Author(s), 2025. Published by Cambridge University Press

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Footnotes

The authors would like to thank the Co-Editor and two reviewers for the constructive comments, which helped to substantially improve the article. The first author’s research was partly supported by the BA Talent Development Award (Grant No. TDA21∖210027). The second author’s research was partly supported by the Leverhulme Research Fellowship (Grant No. RF-2023-396∖9), the BA/Leverhulme Small Research Grant (Grant No. SRG1920/100603), and the National Natural Science Foundation of China (Grant No. 72033002).

References

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