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

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Author Info

  • 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)

Abstract

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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Bibliographic Info

Paper provided by School of Economics and Management, University of Aarhus in its series CREATES Research Papers with number 2009-45.

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Length: 34
Date of creation: 01 Sep 2009
Date of revision:
Handle: RePEc:aah:create:2009-45

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Web page: http://www.econ.au.dk/afn/

Related research

Keywords: Central limit theorem; Diffusionmodels; High-frequency data; Marketmicrostructure noise; Non-synchronous trading; Pre-averaging; Realised covariance;

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References

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Citations

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Cited by:
  1. Valeri Voev, 2009. "On the Economic Evaluation of Volatility Forecasts," CREATES Research Papers 2009-56, School of Economics and Management, University of Aarhus.
  2. Roxana Halbleib & Valeri Voev, 2012. "Forecasting Covariance Matrices: A Mixed Frequency Approach," Working Paper Series of the Department of Economics, University of Konstanz 2012-30, Department of Economics, University of Konstanz.
  3. Markus Bibinger & Markus Reiß, 2011. "Spectral estimation of covolatility from noisy observations using local weights," SFB 649 Discussion Papers SFB649DP2011-086, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  4. Jianqing Fan & Yingying Li & Ke Yu, 2012. "Vast Volatility Matrix Estimation Using High-Frequency Data for Portfolio Selection," Journal of the American Statistical Association, American Statistical Association, vol. 107(497), pages 412-428, March.
  5. Sílvia Gonçalves & Ulrich Hounyo & Nour Meddahi, 2013. "Bootstrap inference for pre-averaged realized volatility based on non-overlapping returns," CREATES Research Papers 2013-07, School of Economics and Management, University of Aarhus.
  6. Peter R. Hansen & Asger Lunde & Valeri Voev, 2010. "Realized Beta GARCH: A Multivariate GARCH Model with Realized Measures of Volatility and CoVolatility," CREATES Research Papers 2010-74, School of Economics and Management, University of Aarhus.
  7. Sujin Park & Oliver Linton, 2012. "Estimating the Quadratic Covariation Matrix for an Asynchronously Observed Continuous Time Signal Masked by Additive Noise," FMG Discussion Papers dp703, Financial Markets Group.
  8. Xinghua Zheng & Yingying Li, 2010. "On the estimation of integrated covariance matrices of high dimensional diffusion processes," Papers 1005.1862, arXiv.org, revised Mar 2012.
  9. Neil Shephard & Dacheng Xiu, 2012. "Econometric analysis of multivariate realised QML: efficient positive semi-definite estimators of the covariation of equity prices," Economics Papers 2012-W04, Economics Group, Nuffield College, University of Oxford.
  10. Rasmus Tangsgaard Varneskov, 2011. "Generalized Flat-Top Realized Kernel Estimation of Ex-Post Variation of Asset Prices Contaminated by Noise," CREATES Research Papers 2011-31, School of Economics and Management, University of Aarhus.
  11. Siem Jan Koopman & Marcel Scharth, 2011. "The Analysis of Stochastic Volatility in the Presence of Daily Realised Measures," Tinbergen Institute Discussion Papers 11-132/4, Tinbergen Institute.
  12. Todorov, Viktor & Bollerslev, Tim, 2010. "Jumps and betas: A new framework for disentangling and estimating systematic risks," Journal of Econometrics, Elsevier, vol. 157(2), pages 220-235, August.
  13. Yuta Koike, 2013. "Limit Theorems for the Pre-averaged Hayashi-Yoshida Estimator with Random Sampling," Global COE Hi-Stat Discussion Paper Series gd12-276, Institute of Economic Research, Hitotsubashi University.
  14. 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.
  15. Neil Shephard & Dacheng Xiu, 2012. "Econometric analysis of multivariate realised QML: efficient positive semi-definite estimators of the covariation of equity prices," Economics Series Working Papers 604, University of Oxford, Department of Economics.

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