Robust High-Dimensional Volatility Matrix Estimation for High-Frequency Factor Model

42 Pages Posted: 13 Dec 2017

See all articles by Jianqing Fan

Jianqing Fan

Princeton University - Bendheim Center for Finance

Donggyu Kim

KAIST College of Business

Date Written: April 5, 2017

Abstract

High-frequency financial data allow us to estimate large volatility matrices with relatively short time horizon. Many novel statistical methods have been introduced to address large volatility matrix estimation problems from a high-dimensional Ito process with microstructural noise contamination. Their asymptotic theories require sub-Gaussian or some finite high-order moments assumptions for observed log-returns. These assumptions are at odd with the heavy tail phenomenon that is pandemic in financial stock returns and new procedures are needed to mitigate the influence of heavy tails. In this paper, we introduce the Huber loss function with a diverging threshold to develop a robust realized volatility estimation. We show that it has the sub-Gaussian concentration around the volatility with only finite fourth moments of observed log-returns. With the proposed robust estimator as input, we further regularize it by using the principal orthogonal component thresholding (POET) procedure to estimate the large volatility matrix that admits an approximate factor structure. We establish the asymptotic theories for such low-rank plus sparse matrices. The simulation study is conducted to check the finite sample performance of the proposed estimation methods.

Keywords: Concentration inequality; Huber loss; low-rank matrix; pre-averaging; spasrity

JEL Classification: C14; C55; C58

Suggested Citation

Fan, Jianqing and Kim, Donggyu, Robust High-Dimensional Volatility Matrix Estimation for High-Frequency Factor Model (April 5, 2017). Available at SSRN: https://ssrn.com/abstract=3085690 or http://dx.doi.org/10.2139/ssrn.3085690

Jianqing Fan

Princeton University - Bendheim Center for Finance ( email )

26 Prospect Avenue
Princeton, NJ 08540
United States
609-258-7924 (Phone)
609-258-8551 (Fax)

HOME PAGE: http://orfe.princeton.edu/~jqfan/

Donggyu Kim (Contact Author)

KAIST College of Business ( email )

85 Hoegiro Dongdaemun-Gu
Seoul 130-722, 130-722
Korea, Republic of (South Korea)

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