Template-type: ReDIF-Paper 1.0
Author-Name: Neil Shephard
Author-Email: neil.shephard@economics.ox.ac.uk
Author-Workplace-Name: Nuffield College, Dept of Economics and Oxford-Man Institute of Quantitative Finance, University of Oxford.
Author-Name: Dacheng Xiu
Author-Email: dacheng.xiu@chicagobooth.edu
Author-Workplace-Name: University of Chicago Booth School of Business
Title: Econometric analysis of multivariate realised QML: efficient positive semi-definite estimators of the covariation of equity prices
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.
Classification-JEL: C01; C14; C58; D53; D81
Length: 41 pages
Creation-Date: 2012-04-23
Number: 2012-W04
File-URL: http://www.nuffield.ox.ac.uk/economics/papers/2012/sx120423.pdf
File-Format: application/pdf
Handle: RePEc:nuf:econwp:1204