Missing in Asynchronicity: A Kalman-EM Approach for Multivariate Realized Covariance Estimation
32 Pages Posted: 9 Feb 2012 Last revised: 11 Sep 2013
Date Written: September 2013
Motivated by the need of an unbiased and positive-semidefinite estimator of multivariate realized covariance matrices, we model noisy and asynchronous ultra-high-frequency asset prices in a state-space framework with missing data. We then estimate the covariance matrix of the latent states through a Kalman smoother and Expectation Maximization (KEM) algorithm. Iterating between the two EM steps, we obtain a covariance matrix estimate which is robust to both asynchronicity and microstructure noise, and positive-semidefinite by construction. We show the performance of the KEM estimator using extensive Monte Carlo simulations mimicking the liquidity and market microstructure characteristics of the S&P 500 universe as well as in an high-dimensional application on US stocks: KEM provides very accurate covariance matrix estimates and significantly outperforms alternative approaches recently introduced in the literature.
Keywords: High frequency data, Realized covariance matrix, Market microstructure noise, Missing data, Kalman filter, EM algorithm, Maximum likelihood
JEL Classification: C13, C51, C52, C58
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