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

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.