Statistics and Its Interface

Volume 6 (2013)

Number 4

A state space model approach to integrated covariance matrix estimation with high frequency data

Pages: 463 – 475



Cheng Liu (Sim Kee Boon Institute for Financial Economics, Singapore Management University, Singapore)

Cheng Yong Tang (Business School, University of Colorado, Denver, Col., U.S.A.)


We consider a state space model approach for high frequency financial data analysis. An expectation-maximization (EM) algorithm is developed for estimating the integrated covariance matrix of the assets. The state space model with the EM algorithm can handle noisy financial data with correlated microstructure noises. Difficulty due to asynchronous and irregularly spaced trading data of multiple assets can be naturally overcome by considering the problem in a scenario with missing data. Since the state space model approach requires no data synchronization, no record in the financial data is deleted so that it efficiently incorporates information from all observations. Empirical data analysis supports the general specification of the state space model, and simulations confirm the efficiency gain and the benefit of the state space model approach.


EM algorithm, high frequency data, integrated covariance matrix, Kalman filter, microstructure noise, missing data, quasi-maximum likelihood, state space model

Full Text (PDF format)