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

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Author Info

  • Corsi, Fulvio

    ()

  • Peluso, Stefano

    ()

  • Audrino, Francesco

    ()

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.

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Bibliographic Info

Paper provided by University of St. Gallen, School of Economics and Political Science in its series Economics Working Paper Series with number 1202.

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Length: 32 pages
Date of creation: Jan 2012
Date of revision:
Handle: RePEc:usg:econwp:2012:02

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Related research

Keywords: High frequency data; Realized covariance matrix; Market microstructure noise; Missing data; Kalman filter; EM algorithm; Maximum likelihood;

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References

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Citations

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Cited by:
  1. Yuta Koike, 2013. "Limit Theorems for the Pre-averaged Hayashi-Yoshida Estimator with Random Sampling," Global COE Hi-Stat Discussion Paper Series gd12-276, Institute of Economic Research, Hitotsubashi University.
  2. Neil Shephard & Dacheng Xiu, 2012. "Econometric analysis of multivariate realised QML: efficient positive semi-definite estimators of the covariation of equity prices," Economics Series Working Papers 604, University of Oxford, Department of Economics.
  3. Fengler, Matthias & Okhrin, Ostap, 2012. "Realized Copula," Economics Working Paper Series 1214, University of St. Gallen, School of Economics and Political Science.

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