Econometric Analysis of Multivariate Realised QML: Estimation of the Covariation of Equity Prices under Asynchronous Trading

53 Pages Posted: 26 Apr 2012 Last revised: 5 Dec 2016

Neil Shephard

Harvard University

Dacheng Xiu

University of Chicago - Booth School of Business

Date Written: December 2, 2016

Abstract

Estimating the covariance between assets using high frequency data is challenging due to market microstructure effects and asynchronous trading. In this paper we develop a multivariate realised quasi maximum likelihood (QML) approach, carrying out inference as if the observations arise from an asynchronously observed vector scaled Brownian model observed with error. Under stochastic volatility the resulting realised QML estimator is positive 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. We also propose an alternative estimator using a factor model, which scales well with the number of assets. We derive the theoretical properties of these estimators and prove that they achieve the efficient rate of convergence. Our estimators are also analysed using Monte Carlo methods and applied to equity data with varying levels of liquidity.

Keywords: EM algorithm, Kalman filter, market microstructure noise, non-synchronous data, quasi-likelihood, semimartingale

JEL Classification: C01, C14, C58, D53, D81

Suggested Citation

Shephard, Neil and Xiu, Dacheng, Econometric Analysis of Multivariate Realised QML: Estimation of the Covariation of Equity Prices under Asynchronous Trading (December 2, 2016). Chicago Booth Research Paper No. 12-14. Available at SSRN: https://ssrn.com/abstract=2045571 or http://dx.doi.org/10.2139/ssrn.2045571

Neil Shephard

Harvard University ( email )

1875 Cambridge Street
Cambridge, MA 02138
United States

Dacheng Xiu (Contact Author)

University of Chicago - Booth School of Business ( email )

5807 S. Woodlawn Avenue
Chicago, IL 60637
United States

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