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Missing in Asynchronicity: A Kalman-EM Approach for Multivariate Realized Covariance Estimation

Francesco Audrino, Fulvio Corsi & Stefano Peluso

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abstract Motivated by the need for 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. In the expectation step, by means of the Kalman filter with missing data, we reconstruct the smoothed and synchronized series of the latent price processes. In the maximization step, we search for covariance matrices that maximize the expected likelihood obtained with the reconstructed price series. Iterating between the two EM steps, we obtain a KEM-improved covariance matrix estimate which is robust to both asynchronicity and microstructure noise, and positive-semidefinite by construction.
Extensive Monte Carlo simulations show the superior performance of the KEM estimator over several alternative covariance matrix estimates introduced in the literature. The application of the KEM estimator in practice is illustrated on a 10-dimensional US stock data set.
   
type working paper (English)
   
keywords High frequency data; Realized covariance matrix; Market microstructure noise; Missing data; Kalman filter; EM algorithm; Maximum likelihood
   
date of appearance 2012
publisher SEPS Working Paper Series (St. Gallen)
review not reviewed
   
profile area SEPS - Quantitative Economic Methods
citation Audrino, F., Corsi, F., & Peluso, S. (2012). Missing in Asynchronicity: A Kalman-EM Approach for Multivariate Realized Covariance Estimation. St. Gallen: SEPS Working Paper Series.