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

32 Pages Posted: 9 Feb 2012 Last revised: 11 Sep 2013

See all articles by Fulvio Corsi

Fulvio Corsi

University of Pisa - Department of Economics; City University London

Stefano Peluso

University of Lugano and Swiss Finance Institute

Francesco Audrino

University of St. Gallen

Date Written: September 2013

Abstract

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

Suggested Citation

Corsi, Fulvio and Peluso, Stefano and Audrino, Francesco, Missing in Asynchronicity: A Kalman-EM Approach for Multivariate Realized Covariance Estimation (September 2013). Available at SSRN: https://ssrn.com/abstract=2000996 or http://dx.doi.org/10.2139/ssrn.2000996

Fulvio Corsi

University of Pisa - Department of Economics ( email )

via Ridolfi 10
I-56100 Pisa, PI 56100
Italy

HOME PAGE: http://people.unipi.it/fulvio_corsi/

City University London ( email )

Northampton Square
London, EC1V OHB
United Kingdom

Stefano Peluso (Contact Author)

University of Lugano and Swiss Finance Institute ( email )

c/o University of Geneva
40, Bd du Pont-d'Arve
CH-1211 Geneva 4
Switzerland

Francesco Audrino

University of St. Gallen ( email )

Bodanstrasse 6
St. Gallen, CH-9000
Switzerland

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