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A Bayesian High-Frequency Estimator of the Multivariate Covariance of Noisy and Asynchronous Returns

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  • Stefano Peluso
  • Fulvio Corsi
  • Antonietta Mira

Abstract

A multivariate positive definite estimator of the integrated covariance matrix of noisy and asynchronously observed asset returns is proposed. We adopt a Bayesian Dynamic Linear Model where microstructure noise is interpreted as measurement error, and asynchronous trading as missing observations in an otherwise synchronous series. Missing observations are treated as any other parameter, as typical in a Bayesian framework. An augmented Gibbs algorithm is used since all full conditionals are available and its convergence and robustness are discussed. A realistic simulation study compares our estimator with existing alternatives, under different liquidity and microstructure noise conditions. The results suggest that our estimator is superior in terms of RMSE particularly under severe conditions, such as portfolios of assets with heterogeneous liquidity and high level of microstructure noise. The application to the empirical dataset of ten tick-by-tick stock price series confirms the simulation results.

Suggested Citation

  • Stefano Peluso & Fulvio Corsi & Antonietta Mira, 2015. "A Bayesian High-Frequency Estimator of the Multivariate Covariance of Noisy and Asynchronous Returns," Journal of Financial Econometrics, Oxford University Press, vol. 13(3), pages 665-697.
    • Handle: RePEc:oup:jfinec:v:13:y:2015:i:3:p:665-697.
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    File URL: http://hdl.handle.net/10.1093/jjfinec/nbu017
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    References listed on IDEAS

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    1. Francesco Audrino & Fabio Trojani, 2011. "A General Multivariate Threshold GARCH Model With Dynamic Conditional Correlations," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 29(1), pages 138-149, January.
    2. Sujin Park & Oliver Linton, 2012. "Estimating the Quadratic Covariation Matrix for an Asynchronously Observed Continuous Time Signal Masked by Additive Noise," FMG Discussion Papers dp703, Financial Markets Group.
    3. Neil Shephard & Dacheng Xiu, 2012. "Econometric analysis of multivariate realised QML: efficient positive semi-definite estimators of the covariation of equity prices," Economics Papers 2012-W04, Economics Group, Nuffield College, University of Oxford.
    4. Fulvio Corsi & Stefano Peluso & Francesco Audrino, 2015. "Missing in Asynchronicity: A Kalman‐em Approach for Multivariate Realized Covariance Estimation," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 30(3), pages 377-397, April.
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    Cited by:

    1. Xin Jin & Jia Liu & Qiao Yang, 2021. "Does the Choice of Realized Covariance Measures Empirically Matter? A Bayesian Density Prediction Approach," Econometrics, MDPI, vol. 9(4), pages 1-22, December.

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