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

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