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

Author

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  • Neil Shephard

    () (Nuffield College, Dept of Economics and Oxford-Man Institute of Quantitative Finance, University of Oxford.)

  • Dacheng Xiu

    () (University of Chicago Booth School of Business)

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 Papers 2012-W04, Economics Group, Nuffield College, University of Oxford.
  • Handle: RePEc:nuf:econwp:1204
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    References listed on IDEAS

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    1. Andersen T. G & Bollerslev T. & Diebold F. X & Labys P., 2001. "The Distribution of Realized Exchange Rate Volatility," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 42-55, March.
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    4. Barndorff-Nielsen, Ole E. & Hansen, Peter Reinhard & Lunde, Asger & Shephard, Neil, 2011. "Multivariate realised kernels: Consistent positive semi-definite estimators of the covariation of equity prices with noise and non-synchronous trading," Journal of Econometrics, Elsevier, vol. 162(2), pages 149-169, June.
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    1. repec:cte:wsrepe:es142416 is not listed on IDEAS
    2. 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.
    3. Veredas, David & Vander Elst, Harry, 2014. "Disentangled jump-robust realized covariances and correlations with non-synchronous prices," DES - Working Papers. Statistics and Econometrics. WS ws142416, Universidad Carlos III de Madrid. Departamento de Estadística.
    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.

    More about this item

    Keywords

    EM algorithm; Kalman filter; market microstructure noise; non-synchronous data; portfolio optimisation; quadratic variation; quasi-likelihood; semimartingale; volatility.;

    JEL classification:

    • C01 - Mathematical and Quantitative Methods - - General - - - Econometrics
    • 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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