High-Dimensional Volatility Matrix Estimation with Cross-Sectional Dependent and Heavy-Tailed Microstructural Noise

Liang, Wanwan1; Wu, Ben1; Fan, Xinyan1; Jing, Bingyi2; Zhang, Bo1

2023-10-01

10.1007/s11424-023-2080-5

JOURNAL OF SYSTEMS SCIENCE & COMPLEXITY   Impact Factor & Quartile

1009-6124

1559-7067

The estimates of the high-dimensional volatility matrix based on high-frequency data play a pivotal role in many financial applications. However, most existing studies have been built on the sub-Gaussian and cross-sectional independence assumptions of microstructure noise, which are typically violated in the financial markets. In this paper, the authors proposed a new robust volatility matrix estimator, with very mild assumptions on the cross-sectional dependence and tail behaviors of the noises, and demonstrated that it can achieve the optimal convergence rate n-1/4. Furthermore, the proposed model offered better explanatory and predictive powers by decomposing the estimator into low-rank and sparse components, using an appropriate regularization procedure. Simulation studies demonstrated that the proposed estimator outperforms its competitors under various dependence structures of microstructure noise. Additionally, an extensive analysis of the high-frequency data for stocks in the Shenzhen Stock Exchange of China demonstrated the practical effectiveness of the estimator.

Cross-sectional dependence high-dimensional data high-frequency data integrated volatility matrix market microstructure noise

SCI

English

Others

National Natural Science Foundation of China["72271232","71873137"] ; MOE Project of Key Research Institute of Humanities and Social Sciences[22JJD110001]

Mathematics

Mathematics, Interdisciplinary Applications

WOS:001085954700017

SPRINGER HEIDELBERG

Web of Science

1.Renmin Univ China, Inst Probabil & Stat, Sch Stat, Ctr Appl Stat, Beijing 100086, Peoples R China
2.Southern Univ Sci & Technol, Dept Stat & Data Sci, Shenzhen 518055, Peoples R China

Liang, Wanwan,Wu, Ben,Fan, Xinyan,et al. High-Dimensional Volatility Matrix Estimation with Cross-Sectional Dependent and Heavy-Tailed Microstructural Noise[J]. JOURNAL OF SYSTEMS SCIENCE & COMPLEXITY,2023,36(5).

Liang, Wanwan,Wu, Ben,Fan, Xinyan,Jing, Bingyi,&Zhang, Bo.(2023).High-Dimensional Volatility Matrix Estimation with Cross-Sectional Dependent and Heavy-Tailed Microstructural Noise.JOURNAL OF SYSTEMS SCIENCE & COMPLEXITY,36(5).

Liang, Wanwan,et al."High-Dimensional Volatility Matrix Estimation with Cross-Sectional Dependent and Heavy-Tailed Microstructural Noise".JOURNAL OF SYSTEMS SCIENCE & COMPLEXITY 36.5(2023).