Nonparametric Estimation of Large Spot Volatility Matrices for High-Frequency Financial Data
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Authors
Bu, R.
Li, D.
Linton, O.
Wang, H.
Publication Date
2022-03-16Series
Cambridge Working Papers in Economics
Janeway Institute Working Paper Series
Publisher
Faculty of Economics, University of Cambridge
Type
Working Paper
Metadata
Show full item recordCitation
Bu, R., Li, D., Linton, O., & Wang, H. (2022). Nonparametric Estimation of Large Spot Volatility Matrices for High-Frequency Financial Data. https://doi.org/10.17863/CAM.83981
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 generalised 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 the highfrequency data contaminated by the microstructure noise, we introduce a localised pre-averaging estimation method in the high-dimensional setting which first pre-whitens data via a kernel filter and then uses the estimation tool developed in the noise-free scenario, and further derive the uniform convergence rates for the developed spot volatility matrix estimator. In addition, we also combine the kernel smoothing with the shrinkage technique to estimate the time-varying volatility matrix of the high-dimensional noise vector, and establish the relevant uniform consistency result. Numerical studies are provided to examine performance of the proposed estimation methods in finite samples.
Keywords
Brownian semi-martingale, Kernel smoothing, Microstructure noise, Sparsity, Spot volatility matrix, Uniform consistency
Identifiers
CWPE2218, JIWP2208
This record's DOI: https://doi.org/10.17863/CAM.83981
This record's URL: https://www.repository.cam.ac.uk/handle/1810/336560
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