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

Neil Shephard () and Dacheng Xiu ()
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Dacheng Xiu: University of Chicago Booth School of Business

No 2012-W04, Economics Papers from Economics Group, Nuffield College, University of Oxford

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.

Keywords: EM algorithm; Kalman filter; market microstructure noise; non-synchronous data; portfolio optimisation; quadratic variation; quasi-likelihood; semimartingale; volatility. (search for similar items in EconPapers)
JEL-codes: C01 C14 C58 D53 D81 (search for similar items in EconPapers)
Pages: 41 pages
Date: 2012-04-23
New Economics Papers: this item is included in nep-ecm, nep-mst and nep-ore
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Citations: View citations in EconPapers (6)

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Working Paper: Econometric analysis of multivariate realised QML: efficient positive semi-definite estimators of the covariation of equity prices (2012)
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