Econometric Analysis of Multivariate Realised QML: Estimation of the Covariation of Equity Prices under Asynchronous Trading
University of Oxford - Oxford-Man Institute; University of Oxford - Nuffield College; University of Oxford - Oxford Financial Research Centre
University of Chicago - Booth School of Business
October 22, 2012
Chicago Booth Research Paper No. 12-14
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 optimized 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 analyzed using Monte Carlo methods and applied on equity data that are distinct in their levels of liquidity.
Number of Pages in PDF File: 56
Keywords: EM algorithm, Kalman filter, market microstructure noise, non-synchronous data, portfolio optimization, quadratic variation, quasi-likelihood, semimartingale, volatility
JEL Classification: C01, C14, C58, D53, D81working papers series
Date posted: April 26, 2012 ; Last revised: November 11, 2012
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