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Estimating the Quadratic Covariation Matrix for an Asynchronously Observed Continuous Time Signal Masked by Additive Noise

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  • Sujin Park
  • Oliver Linton

Abstract

We propose a new estimator of multivariate ex-post volatility that is robust to microstructure noise and asynchronous data timing. The method is based on Fourier domain techniques, which have been widely used in discrete time series analysis. The advantage of this method is that it does not require an explicit time alignment, unlike existing methods in the literature. We derive the large sample properties of our estimator under general assumptions allowing for the number of sample points for different assets to be of different order of magnitude. The by-product of our Fourier domain based estimator is that we have a consistent estimator of the instantaneous co-volatility even under the presence of microstructure noise. We show in extensive simulations that our method outperforms the time domain estimator especially when two assets are traded very asynchronously and with different liquidity and when estimating the high dimensional integrated covariance matrix.

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File URL: http://www.lse.ac.uk/fmg/workingPapers/discussionPapers/fmgdps/dp703.pdf
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Bibliographic Info

Paper provided by Financial Markets Group in its series FMG Discussion Papers with number dp703.

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Date of creation: Apr 2012
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Handle: RePEc:fmg:fmgdps:dp703

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Web page: http://www.lse.ac.uk/fmg/

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  1. Yacine Ait-Sahalia & Per A. Mykland & Lan Zhang, 2005. "Ultra High Frequency Volatility Estimation with Dependent Microstructure Noise," NBER Working Papers 11380, National Bureau of Economic Research, Inc.
  2. Kim Christensen & Silja Kinnebrock & Mark Podolskij, 2009. "Pre-averaging estimators of the ex-post covariance matrix in noisy diffusion models with non-synchronous data," CREATES Research Papers 2009-45, School of Economics and Management, University of Aarhus.
  3. Dennis Kristensen, 2007. "Nonparametric Filtering of the Realised Spot Volatility: A Kernel-based Approach," CREATES Research Papers 2007-02, School of Economics and Management, University of Aarhus.
  4. Kalnina, Ilze & Linton, Oliver, 2008. "Estimating quadratic variation consistently in the presence of endogenous and diurnal measurement error," Journal of Econometrics, Elsevier, vol. 147(1), pages 47-59, November.
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Cited by:
  1. Markus Bibinger & Lars Winkelmann, 2013. "Econometrics of co-jumps in high-frequency data with noise," SFB 649 Discussion Papers SFB649DP2013-021, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  2. Markus Bibinger & Per A. Mykland, 2013. "Inference for Multi-Dimensional High-Frequency Data: Equivalence of Methods, Central Limit Theorems, and an Application to Conditional Independence Testing," SFB 649 Discussion Papers SFB649DP2013-006, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.

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