An estimator of the ex-post covariation of log-prices under asynchronicity and microstructure noise is proposed. It uses the Cholesky factorization of the covariance matrix in order to exploit the heterogeneity in trading intensities to estimate the different parameters sequentially with as many observations as possible. The estimator is positive semidefinite by construction. We derive asymptotic results and confirm their good finite sample properties by means of a Monte Carlo simulation. In the application we forecast portfolio Value-at-Risk and sector risk exposures for a portfolio of 52 stocks. We find that the dynamic models utilizing the proposed high-frequency estimator provide statistically and economically superior forecasts.

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Keywords Cholesky decomposition, Integrated covariance, Non-synchronous trading, Positive semidefinite, Realized covariance
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Journal Journal of Econometrics
Boudt, K. (Kris), Laurent, S. (Sébastien), Lunde, A. (Asger), Quaedvlieg, R. (Rogier), & Sauri, O. (Orimar). (2017). Positive semidefinite integrated covariance estimation, factorizations and asynchronicity. Journal of Econometrics, 196(2), 347–367. doi:10.1016/j.jeconom.2016.09.016