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

  • Neil Shephard
  • Dacheng Xiu

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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Paper provided by University of Oxford, Department of Economics in its series Economics Series Working Papers with number 604.

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Date of creation: 01 Apr 2012
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Handle: RePEc:oxf:wpaper:604
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  1. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Paul Labys, 2001. "Modeling and Forecasting Realized Volatility," NBER Working Papers 8160, National Bureau of Economic Research, Inc.
  2. Ole E. Barndorff-Nielsen & Peter Reinhard Hansen & Asger Lunde & Neil Shephard, 2011. "Multivariate realised kernels: Consistent positive semi-definite estimators of the covariation of equity prices with noise and non-synchronous trading," Post-Print hal-00815564, HAL.
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  7. Kim Christensen & Silja Kinnebrock & Mark Podolskij, 2010. "Pre-averaging estimators of the ex-post covariance matrix in noisy diffusion models with non-synchronous data," Post-Print hal-00732537, HAL.
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  15. repec:cep:stiecm:/2006/509 is not listed on IDEAS
  16. Per A. Mykland & Lan Zhang, 2009. "Inference for Continuous Semimartingales Observed at High Frequency," Econometrica, Econometric Society, vol. 77(5), pages 1403-1445, 09.
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