Large-Dimensional Positive Definite Covariance Estimation for High Frequency Data via Low-rank and Sparse Matrix Decomposition

35 Pages Posted: 8 Jul 2019 Last revised: 29 Mar 2021

See all articles by Liyuan Cui

Liyuan Cui

City University of Hong Kong

Yongmiao Hong

Cornell University - Department of Economics

Yingxing Li

Xiamen University

Junhui Wang

City University of Hong Kong (CityU) - School of Data Science

Date Written: March 4, 2019

Abstract

This paper proposes a novel covariance estimator via a machine learning approach when both the sampling frequency and covariance dimension are large. Assuming that a large covariance matrix can be decomposed into low rank and sparse components, our method simultaneously provides a consistent estimation of these two components in a one-step procedure. Moreover, in the presence of microstructure noises and asynchronous trading, the covariance estimator is guaranteed to be positive definite with the optimal rate of convergence. Taking into account the serial dependent feature of financial data, we further provide a data-driven algorithm to select the optimal tuning parameters in practice. We apply the proposed estimator to vast portfolio allocations, which enjoy significantly enhanced out-of-sample portfolio risk and Sharpe ratios. The success of our approach helps justify the role that machine learning techniques play in finance.

Keywords: Machine Learning, Large Covariance, High Frequency, High Dimension, Positive Definite, Vast Portfolio Evaluation, Sharpe Ratios, ADMM

JEL Classification: C13, C14, C55, C58, C61, G01

Suggested Citation

Cui, Liyuan and Hong, Yongmiao and Li, Yingxing and Wang, Junhui, Large-Dimensional Positive Definite Covariance Estimation for High Frequency Data via Low-rank and Sparse Matrix Decomposition (March 4, 2019). Available at SSRN: https://ssrn.com/abstract=3414910 or http://dx.doi.org/10.2139/ssrn.3414910

Liyuan Cui (Contact Author)

City University of Hong Kong ( email )

83 Tat Chee Avenue
Kowloon
Hong Kong

Yongmiao Hong

Cornell University - Department of Economics ( email )

Department of Statistical Science
414 Uris Hall
Ithaca, NY 14853-7601
United States
607-255-5130 (Phone)
607-255-2818 (Fax)

Yingxing Li

Xiamen University ( email )

Xiamen, Fujian 361005
China

Junhui Wang

City University of Hong Kong (CityU) - School of Data Science ( email )

Kowloon
Hong Kong

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