Kim Christensen () (Aarhus University and CREATES) Silja Kinnebrock () (Oxford-Man Institute of Quantitative Finance, Oxford University) Mark Podolskij () (ETH Zürich, Switzerland and CREATES, Aarhus University)
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In this paper, we show how simple pre-averaging can be applied to measure the ex-post covariance of high-frequency financial time series under market microstructure noise and non-synchronous trading. A modulated realised covariance based on pre-averaged data is proposed and studied in this setting, and we provide complete large sample asymptotics for this new estimator, including feasible central limit theorems for standard methods such as covariance, regression, and correlation analysis. We discuss several versions of the modulated realised covariance, which can be designed to possess an optimal rate of convergence or to guarantee positive semi-definite covariance matrix estimates. We also derive a pre-averaged version of the Hayashi-Yoshida estimator that can be applied directly to the noisy and nonsynchronous data without any prior alignment of prices. An empirical study illustrates how high-frequency covariances, regression coefficients, and correlations change through time.
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Paper provided by School of Economics and Management, University of Aarhus in its series CREATES Research Papers with number
2009-45.
Find related papers by JEL classification: C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - General C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions C80 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs - - - General
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References listed on IDEAS Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
Ghysels, E. & Harvey, A. & Renault, E., 1996.
"Stochastic Volatility,"
Cahiers de recherche
9613, Universite de Montreal, Departement de sciences economiques.
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Other versions:
Ghysels, E. & Harvey, A. & Renault, E., 1996.
"Stochastic Volatility,"
Cahiers de recherche
9613, Centre interuniversitaire de recherche en économie quantitative, CIREQ.