Dynamic Covariance Matrix Estimation and Portfolio Analysis with High-Frequency Data

The covariance matrix associated with multiple financial returns plays foundational roles in many empirical applications, for example, quantifying risks and managing investment portfolios. Such covariance matrices are well known to be dynamic, that is, their structures change with the underlying market conditions. To incorporate such dynamics in a setting with high-frequency noisy data contaminated by measurement errors, we propose a new approach for estimating the covariances of a high-dimensional return series. By utilizing an appropriate localization, our approach is designed upon exploiting generic variables that are informative in accounting for the dynamic changes. We then investigate the properties and performance of the high-dimensional minimal-variance sparse portfolio constructed from employing the proposed dynamic covariance estimator. Our theory establishes the validity of the proposed covariance estimation methods in handling high-dimensional, high-frequency noisy data. The promising applications of our methods are demonstrated by extensive simulations and empirical studies showing the satisfactory accuracy of the covariance estimation and the substantially improved portfolio performance.