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Econometric analysis of multivariate realised QML: efficient positive semi-definite estimators of the covariation of equity prices

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  • Neil Shephard
  • Dacheng Xiu

Abstract

Estimating the covariance and correlation between assets using high frequency data is challenging due to market microstructure effects and Epps effects. In this paper we extend Xiu's univariate QML approach to the multivariate case, carrying out inference as if the observations arise from an asynchronously observed vector scaled Brownian model observed with error. Under stochastic volatility the resulting QML estimator is positive semi-definite, uses all available data, is consistent and asymptotically mixed normal. The quasi-likelihood is computed using a Kalman filter and optimised using a relatively simple EM algorithm which scales well with the number of assets. We derive the theoretical properties of the estimator and prove that it achieves the efficient rate of convergence. We show how to make it achieve the non-parametric efficiency bound for this problem. The estimator is also analysed using Monte Carlo methods and applied on equity data that are distinct in their levels of liquidity.

Suggested Citation

  • 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.
  • Handle: RePEc:oxf:wpaper:604
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    References listed on IDEAS

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    Cited by:

    1. Harry-Paul Vander Elst & David Veredas, 2014. "Disentangled Jump-Robust Realized Covariances and Correlations with Non-Synchronous Prices," Working Papers ECARES ECARES 2014-35, ULB -- Universite Libre de Bruxelles.
    2. 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, Society for Financial Econometrics, vol. 13(3), pages 665-697.
    3. repec:cte:wsrepe:es142416 is not listed on IDEAS
    4. Kim, Donggyu & Wang, Yazhen & Zou, Jian, 2016. "Asymptotic theory for large volatility matrix estimation based on high-frequency financial data," Stochastic Processes and their Applications, Elsevier, vol. 126(11), pages 3527-3577.
    5. Yuta Koike, 2014. "An estimator for the cumulative co-volatility of asynchronously observed semimartingales with jumps," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 41(2), pages 460-481, June.
    6. Harry Vander Elst & David Veredas, 2017. "Smoothing it Out: Empirical and Simulation Results for Disentangled Realized Covariances," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 15(1), pages 106-138.

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    More about this item

    Keywords

    EM algorithm; Kalman filter; Market microstructure noise; Non-synchronous data; Portfolio optimisation; Quadratic variation; Quasi-likelihood; Semimartingale; Volatility;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics
    • D53 - Microeconomics - - General Equilibrium and Disequilibrium - - - Financial Markets
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

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