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On covariation estimation for multivariate continuous Itô semimartingales with noise in non-synchronous observation schemes

  • Kim Christensen

    ()

    (Aarhus University and CREATES)

  • Mark Podolskij

    ()

    (University of Heidelberg and CREATES)

  • Mathias Vetter

    ()

    (Ruhr-Universität Bochum, Fakultät für Mathematik)

This paper presents a Hayashi-Yoshida type estimator for the covariation matrix of continuous Itô semimartingales observed with noise. The coordinates of the multivariate process are assumed to be observed at highly frequent nonsynchronous points. The estimator of the covariation matrix is designed via a certain combination of the local averages and the Hayashi-Yoshida estimator. Our method does not require any synchronization of the observation scheme (as e.g. previous tick method or refreshing time method) and it is robust to some dependence structure of the noise process. We show the associated central limit theorem for the proposed estimator and provide a feasible asymptotic result. Our proofs are based on a blocking technique and a stable convergence theorem for semimartingales. Finally, we show simulation results for the proposed estimator to illustrate its finite sample properties.

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Paper provided by School of Economics and Management, University of Aarhus in its series CREATES Research Papers with number 2011-53.

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Length: 42
Date of creation: 02 Dec 2011
Date of revision:
Handle: RePEc:aah:create:2011-53
Contact details of provider: Web page: http://www.econ.au.dk/afn/

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  1. Christensen, Kim & Oomen, Roel & Podolskij, Mark, 2010. "Realised quantile-based estimation of the integrated variance," Journal of Econometrics, Elsevier, vol. 159(1), pages 74-98, November.
  2. Ole E Barndorff-Nielsen & Peter Hansen & Asger Lunde & Neil Shephard, 2006. "Designing realised kernels to measure the ex-post variation of equity prices in the presence of noise," OFRC Working Papers Series 2006fe05, Oxford Financial Research Centre.
  3. Bandi, Federico M. & Russell, Jeffrey R., 2006. "Separating microstructure noise from volatility," Journal of Financial Economics, Elsevier, vol. 79(3), pages 655-692, March.
  4. Ole E. Barndorff-Nielsen & Peter Reinhard Hansen & Asger Lunde & Neil Shephard, 2008. "Multivariate realised kernels: consistent positive semi-definite estimators of the covariation of equity prices with noise and non-synchronous trading," CREATES Research Papers 2008-63, School of Economics and Management, University of Aarhus.
  5. Zhang, Lan & Mykland, Per A. & Ait-Sahalia, Yacine, 2005. "A Tale of Two Time Scales: Determining Integrated Volatility With Noisy High-Frequency Data," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 1394-1411, December.
  6. Mark Podolskij & Mathias Vetter, 2008. "Bipower-type estimation in a noisy diffusion setting," CREATES Research Papers 2008-25, School of Economics and Management, University of Aarhus.
  7. Jacod, Jean & Li, Yingying & Mykland, Per A. & Podolskij, Mark & Vetter, Mathias, 2009. "Microstructure noise in the continuous case: The pre-averaging approach," Stochastic Processes and their Applications, Elsevier, vol. 119(7), pages 2249-2276, July.
  8. Kim Christensen & Silja Kinnebrock & Mark Podolskij, 2010. "Pre-averaging estimators of the ex-post covariance matrix in noisy diffusion models with non-synchronous data," Post-Print hal-00732537, HAL.
  9. Markus Bibinger, 2011. "Efficient Covariance Estimation for Asynchronous Noisy High‐Frequency Data," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 38(1), pages 23-45, 03.
  10. Jacod, Jean, 2008. "Asymptotic properties of realized power variations and related functionals of semimartingales," Stochastic Processes and their Applications, Elsevier, vol. 118(4), pages 517-559, April.
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