Abstract

http://ssrn.com/abstract=2045571
 


 



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


Neil Shephard


University of Oxford - Oxford-Man Institute; University of Oxford - Nuffield College; University of Oxford - Oxford Financial Research Centre

Dacheng Xiu


University of Chicago - Booth School of Business

October 22, 2012

Chicago Booth Research Paper No. 12-14

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 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, D81

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Date posted: April 26, 2012 ; Last revised: November 11, 2012

Suggested Citation

Shephard, Neil and Xiu, Dacheng, Econometric Analysis of Multivariate Realised QML: Estimation of the Covariation of Equity Prices under Asynchronous Trading (October 22, 2012). Chicago Booth Research Paper No. 12-14. Available at SSRN: http://ssrn.com/abstract=2045571 or http://dx.doi.org/10.2139/ssrn.2045571

Contact Information

Neil Shephard
University of Oxford - Oxford-Man Institute ( email )
Eagle House
Walton Well Road
Oxford, Oxfordshire OX2 6ED
United Kingdom
44 1865 616600 (Phone)
44 1865 616601 (Fax)
HOME PAGE: http://www.oxford-man.ox.ac.uk
University of Oxford - Nuffield College ( email )
New Road
Oxford, OX1 1NF
United Kingdom
44 1865 278593 (Phone)
44 1865 278500 (Fax)
University of Oxford - Oxford Financial Research Centre ( email )
Oxford
United Kingdom
HOME PAGE: http://www.finance.ox.ac.uk
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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