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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

    ()
    (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.

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Bibliographic Info

Paper provided by Economics Group, Nuffield College, University of Oxford in its series Economics Papers with number 2012-W04.

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Length: 41 pages
Date of creation: 23 Apr 2012
Date of revision:
Handle: RePEc:nuf:econwp:1204

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Web page: http://www.nuff.ox.ac.uk/economics/

Related research

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

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  2. Ole E. Barndorff-Nielsen & Peter Reinhard Hansen & Asger Lunde & Neil Shephard, 2008. "Multivariate realised kernels: consistent positive semi-definite estimators of the covariation of equity prices with noise and non-synchronous trading," Economics Papers, Economics Group, Nuffield College, University of Oxford 2008-W10, Economics Group, Nuffield College, University of Oxford.
  3. Jacod, Jean & Li, Yingying & Mykland, Per A. & Podolskij, Mark & Vetter, Mathias, 2009. "Microstructure noise in the continuous case: The pre-averaging approach," Stochastic Processes and their Applications, Elsevier, Elsevier, vol. 119(7), pages 2249-2276, July.
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  13. Zhang, Lan, 2011. "Estimating covariation: Epps effect, microstructure noise," Journal of Econometrics, Elsevier, Elsevier, vol. 160(1), pages 33-47, January.
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