Nonparametric Estimation of Large Spot Volatility Matrices for High-Frequency Financial Data

Ruijun Bu, Degui Li, Oliver Linton and Hanchao Wang

Janeway Institute Working Papers from Faculty of Economics, University of Cambridge

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 (search for similar items in EconPapers)
JEL-codes: C10 C14 C22 (search for similar items in EconPapers)
Date: 2022-03-16
New Economics Papers: this item is included in nep-ban, nep-ecm, nep-ets, nep-mst, nep-ore and nep-rmg
Note: obl20
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https://www.janeway.econ.cam.ac.uk/working-paper-pdfs/jiwp2208.pdf

Related works:
Working Paper: Nonparametric Estimation of Large Spot Volatility Matrices for High-Frequency Financial Data (2023)
Working Paper: Nonparametric Estimation of Large Spot Volatility Matrices for High-Frequency Financial Data (2022)
Working Paper: Nonparametric Estimation of Large Spot Volatility Matrices for High-Frequency Financial Data (2022)
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Persistent link: https://EconPapers.repec.org/RePEc:cam:camjip:2208

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