Pre-Averaging Estimators of the Ex-Post Covariance Matrix in Noisy Diffusion Models with Non-Synchronous Data

By Kim Christensen, Silja Kinnebrock, Mark Podolskij. 2010

245 citations recorded by the source corpus.

We 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.

Subfields: Economics and Econometrics, Finance

View Paper: https://www.semanticscholar.org/paper/0ff34fcd855416ac702fc1949956cc23473b567f

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Citations in the corpus

On the number of common factors with high‐frequency data (2017, methodology): “Pre-averaging was later extended by Christensen et al. (2010) to estimate integrated volatility matrices of finite dimension.”
Realized Wishart-Garch: A Score-Driven Multi-Asset Volatility Model (2016, unknown): “In the case of multiple assets, realized measures of asset covariance have also been proposed and considered; see Christensen, Kinnebrock, and Podolskij (2010), Barndorff-Nielsen et al. (2011a), Griffin and Oomen (2011), and references therein.”
Incorporating Global Industrial Classification Standard Into Portfolio Allocation: A Simple Factor-Based Large Covariance Matrix Estimator With High-Frequency Data (2016, unknown): “Notable references include: Aı̈t-Sahalia, Fan, and Xiu (2010), Christensen, Kinnebrock, and Podolskij (2010), BarndorffNielsen et al. (2011), Zhang (2011), Shephard and Xiu (2012), and Bibinger et al. (2014).”
Econometric Analysis of Vast Covariance Matrices Using Composite Realized Kernels and Their Application to Portfolio Choice (2016, methodology): “using low-frequency data, Brownlees & Engle (2010) portray the importance of modelling conditional correlations for systemic risk management, where they show that a rise in a firm’s stock volatility and correlation with the market magnifies its contribution to their proposed measure of systemic risk”
Using Principal Component Analysis to Estimate a High Dimensional Factor Model with High-Frequency Data (2017, methodology): “Various methods are available, including Hayashi and Yoshida (2005), Aı̈t-Sahalia et al. (2010), Christensen et al. (2010), Barndorff-Nielsen et al. (2011), Zhang (2011), Shephard and Xiu (2012) and Bibinger et al. (2014).”
An estimator for the quadratic covariation of asynchronously observed Itô processes with noise: Asymptotic distribution theory (2011, methodology): “Alternative approaches to similar statistical models has been suggested by [5], [9] and [1].”
Outlyingness weighted covariation (2011, unknown): “This value is of the same order as the noise ratios reported in Table 1 of Christensen et al. (2010) for S&P 500 stocks in 2006.”
REALIZED BETA GARCH: A MULTIVARIATE GARCH MODEL WITH REALIZED MEASURES OF VOLATILITY (2012, background): “Estimators that are robust to noise and/or asynchronous observations have been proposed by Hayashi and Yoshida (2005), Voev and Lunde (2007), Griffin and Oomen (2011), Christensen et al. (2010), and Barndorff-Nielsen et al. (2011).”
Is the diurnal pattern sufficient to explain intraday variation in volatility? A nonparametric assessment (2017, unknown): “24 We pre-average using (17) and (37), which we do locally on a window of size We work with θ = 1 / 3 and θ = 1 (as also done in, e.g., Christensen, Kinnebrock, and Podolskij, 2010).”
Interconnectedness in the global financial market (2017, unknown): “This procedure is related to the works by Christensen et al. (2010) and Hayashi and Yoshida (2008), albeit much simpler and to be understood as an approximation.”