Pre-averaging estimators of the ex-post covariance matrix in noisy diffusion models with non-synchronous data

Abstract

International audienceWe show how pre-averaging can be applied to the problem of measuring the ex-post covariance of financial asset returns under microstructure noise and non-synchronous trading. A pre-averaged realised covariance is proposed, and we present an asymptotic theory for this new estimator, which can be configured to possess an optimal convergence rate or to ensure positive semi-definite covariance matrix estimates. We also derive a noise-robust Hayashi-Yoshida estimator that can be implemented on the original data without prior alignment of prices. We uncover the finite sample properties of our estimators with simulations and illustrate their practical use on high-frequency equity data

Econometric analysis of multivariate realised QML: Estimation of the covariation of equity prices under asynchronous trading

“…Two deliver positive semi-definite estimators, so allowing correlations and betas to be coherently computed. They are the multivariate realised kernel of Barndorff-Nielsen, Hansen, Lunde, and Shephard (2011) and the non-biased corrected preaveraging estimator of Christensen, Kinnebrock, and Podolskij (2010). Both use so-called refresh time sampling, suggested first in this context by the former paper.…”

“…The papers are Aït-Sahalia, Fan, and Xiu (2010) and Zhang (2011). The bias-corrected Christensen, Kinnebrock, and Podolskij (2010) is also not necessarily positive semi-definite. Further, none of them achieve the non-parametric efficiency bound.…”

“…Typically there is a very large drop in the sample size due to synchronisation. The most well known such scheme is the Refresh Time method analysed by Barndorff-Nielsen, Hansen, Lunde, and Shephard (2011) and subsequently employed by, for example, Christensen, Kinnebrock, and Podolskij (2010) and Aït-Sahalia, Fan, and Xiu (2010). See also the earlier more informal papers by Harris, McMcInish, Shoesmith, and Wood (1995) and Martens (2003).…”

Disentangled Jump-Robust Realized Covariances and Correlations with Non-Synchronous Prices

“…following Christensen et al (2010a). The scaling in front of the sum is necessary to avoid insample biases in the estimates.…”

“…Several solutions are provided in the literature both for realized variances and covariances. They include, among others, sparse sampling (Andersen et al (2001) and Bandi and Russell (2008)), multi-scale estimators (Zhang et al (2005) and Zhang (2006)), pre-averaging techniques , , Christensen et al (2010a) and Christensen et al (2013)), realized kernels (Barndorff-Nielsen et al (2008) and Barndorff-Nielsen et al (2011)), pseudo-maximum likelihood techniques (Aït-Sahalia et al (2010)), and measures based on the Kalman filter and the EM algorithm (Shephard and Xiu (2012) and Corsi et al (2012)). …”