Positive Definite High-dimensional Covariance Estimation under a General Factor Model with High-frequency Data

香港城市大学经济与金融系助理教授。2010年本科毕业于武汉大学数学与应用数学专业，2017年获得美国康奈尔大学经济学博士学位。主要研究方向包括金融计量经济学、高维协方差矩阵分析、高频交易、非参数统计建模等。

This paper proposes a novel large-dimensional positive definite covariance (LDPDC) estimator for high-frequency data under a general factor model framework. We demonstrate an appealing connection between LDPDC and a weighted group LASSO penalized least squares estimator. LDPDC improves the traditional principal component analysis by allowing for weak factors, whose signal strengths are relatively weak compared to the idiosyncratic component.  Even when microstructure noise and asynchronous trading are present, LDPDC achieves a guarded positive definiteness without deteriorating convergence rates. To make LDPDC fully operational, we provide an extended simultaneous alternating direction method of multipliers algorithm to solve the resultant constrained convex minimization problem. We offer a data-driven algorithm to select involved tuning parameters in practice optimally. Empirically, we study the monthly high-frequency covariance structure of the stock constituents of the S&P 500 index from 2008 to 2016, based on which we construct statistical high-frequency factor returns. We use all traded stocks from NYSE, AMEX, and NASDAQ stock markets to construct 12 high-frequency firm characteristic-based economic factors. We further examine the out-of-sample performance of LDPDC through vast portfolio allocations, which deliver significantly reduced out-of-sample portfolio risk and enhanced Sharpe ratios. The success of our approach helps justify the usefulness of machine learning techniques in finance.