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

LIANG Wanwan, WU Ben, FAN Xinyan, JING Bingyi, ZHANG Bo

Journal of Systems Science & Complexity ›› 2023, Vol. 36 ›› Issue (5) : 2125-2154.

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中国科学院数学与系统科学研究院期刊网
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Journal of Systems Science & Complexity ›› 2023, Vol. 36 ›› Issue (5) : 2125-2154. DOI: 10.1007/s11424-023-2080-5

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

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Abstract

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.

Key words

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

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LIANG Wanwan , WU Ben , FAN Xinyan , JING Bingyi , ZHANG Bo. High-Dimensional Volatility Matrix Estimation with Cross-Sectional Dependent and Heavy-Tailed Microstructural Noise. Journal of Systems Science and Complexity, 2023, 36(5): 2125-2154 https://doi.org/10.1007/s11424-023-2080-5

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Funding

The research of Bo Zhang is supported by the National Natural Science Foundation of China under Grant Nos. 72271232, 71873137 and the MOE Project of Key Research Institute of Humanities and Social Sciences under Grant No. 22JJD110001. The authors gratefully acknowledge the support of Public Computing Cloud, Renmin University of China.
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