Covariance Matrix Estimation with High Frequency Financial Data

Abstract

Estimating the integrated covariance matrix (ICM) from high frequency financial trading data is crucial to reflect the volatilities and covariations of trading instruments. Such an objective is difficult due to contaminated data with microstructure noises, asynchronous trading records, and increasing data dimensionality. In this paper, we study a quasi-maximum likelihood (QML) approah and a QKF approach, which is a combination of QML and Kalman filter, for estimating an ICM. We demonstrate that the QML and QKF estimators are consistent to the ICM, and are asymptotically normally distributed. Efficiency gain of the two approaches is theoretically quantified, and numerically demonstrated via extensive simulation studies. An application of the QML and QKF approaches is illustrated through analyzing a high frequency financial trading data set.