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Estimating covariation: Epps effect, microstructure noise

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  • Zhang, Lan
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    Abstract

    This paper is about how to estimate the integrated covariance T of two assets over a fixed time horizon [0,T], when the observations of X and Y are "contaminated" and when such noisy observations are at discrete, but not synchronized, times. We show that the usual previous-tick covariance estimator is biased, and the size of the bias is more pronounced for less liquid assets. This is an analytic characterization of the Epps effect. We also provide the optimal sampling frequency which balances the tradeoff between the bias and various sources of stochastic error terms, including nonsynchronous trading, microstructure noise, and time discretization. Finally, a two scales covariance estimator is provided which simultaneously cancels (to first order) the Epps effect and the effect of microstructure noise. The gain is demonstrated in data.

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    Bibliographic Info

    Article provided by Elsevier in its journal Journal of Econometrics.

    Volume (Year): 160 (2011)
    Issue (Month): 1 (January)
    Pages: 33-47

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    Handle: RePEc:eee:econom:v:160:y:2011:i:1:p:33-47

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    Web page: http://www.elsevier.com/locate/jeconom

    Related research

    Keywords: Bias-variance tradeoff Epps effect High frequency data Measurement error Market microstructure Martingale Nonsynchronous trading Realized covariance Realized variance Two scales estimation;

    References

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    1. Barndorff-Nielsen, Ole E. & Hansen, Peter Reinhard & Lunde, Asger & Shephard, Neil, 2011. "Subsampling realised kernels," Journal of Econometrics, Elsevier, vol. 160(1), pages 204-219, January.
    2. Ole E. Barndorff-Nielsen & Peter Reinhard Hansen & Asger Lunde & Neil Shephard, 2009. "Multivariate Realised Kernels: Consistent Positive Semi-Definite Estimators of the Covariation of Equity Prices with Noise and Non-Synchronous Trading," Global COE Hi-Stat Discussion Paper Series gd08-037, Institute of Economic Research, Hitotsubashi University.
    3. Ole E. Barndorff-Nielsen & Neil Shephard, 2000. "Econometric analysis of realised volatility and its use in estimating stochastic volatility models," Economics Papers 2001-W4, Economics Group, Nuffield College, University of Oxford, revised 05 Jul 2001.
    4. Zhang, Lan & Mykland, Per A. & Aït-Sahalia, Yacine, 2011. "Edgeworth expansions for realized volatility and related estimators," Journal of Econometrics, Elsevier, vol. 160(1), pages 190-203, January.
    5. Valeri Voev & Asger Lunde, 2007. "Integrated Covariance Estimation using High-frequency Data in the Presence of Noise," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 5(1), pages 68-104.
    6. 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.
    7. 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.
    8. Andrew W. Lo & Craig A. MacKinlay, . "An Econometric Analysis of Nonsyschronous-Trading," Rodney L. White Center for Financial Research Working Papers 19-89, Wharton School Rodney L. White Center for Financial Research.
    9. Jacod, Jean & Li, Yingying & Mykland, Per A. & Podolskij, Mark & Vetter, Mathias, 2007. "Microstructure noise in the continuous case: the pre-averaging approach," Technical Reports 2007,41, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    10. Scholes, Myron & Williams, Joseph, 1977. "Estimating betas from nonsynchronous data," Journal of Financial Economics, Elsevier, vol. 5(3), pages 309-327, December.
    11. Andersen T. G & Bollerslev T. & Diebold F. X & Labys P., 2001. "The Distribution of Realized Exchange Rate Volatility," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 42-55, March.
    12. Andersen, Torben G & Bollerslev, Tim, 1998. "Answering the Skeptics: Yes, Standard Volatility Models Do Provide Accurate Forecasts," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 885-905, November.
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    Citations

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    Cited by:
    1. Mardi Dungey & Lyudmyla Hvozdyk, 2010. "Cojumping: Evidence from the US Treasury Bond and Futures Markets," NCER Working Paper Series 56, National Centre for Econometric Research, revised 20 Jul 2010.
    2. Aït-Sahalia, Yacine & Mykland, Per A. & Zhang, Lan, 2011. "Ultra high frequency volatility estimation with dependent microstructure noise," Journal of Econometrics, Elsevier, vol. 160(1), pages 160-175, January.
    3. Boudt, Kris & Cornelissen, Jonathan & Croux, Christophe, 2012. "Jump robust daily covariance estimation by disentangling variance and correlation components," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 2993-3005.
    4. Jianqing Fan & Yingying Li & Ke Yu, 2010. "Vast Volatility Matrix Estimation using High Frequency Data for Portfolio Selection," Papers 1004.4956, arXiv.org.
    5. Yin Liao & Heather M. Anderson, 2011. "Testing for co-jumps in high-frequency financial data: an approach based on first-high-low-last prices," Monash Econometrics and Business Statistics Working Papers 9/11, Monash University, Department of Econometrics and Business Statistics.
    6. Wang, Kent & Liu, Junwei & Liu, Zhi, 2013. "Disentangling the effect of jumps on systematic risk using a new estimator of integrated co-volatility," Journal of Banking & Finance, Elsevier, vol. 37(5), pages 1777-1786.
    7. Nicolas Huth & Frédéric Abergel, 2011. "High Frequency Lead/lag Relationships - Empirical facts," Working Papers hal-00645685, HAL.
    8. Kris Boudt & Sébastien Laurent & Asger Lunde & Rogier Quaedvlieg, 2014. "Positive Semidefinite Integrated Covariance Estimation, Factorizations and Asynchronicity," CREATES Research Papers 2014-05, School of Economics and Management, University of Aarhus.
    9. 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.
    10. Dovonon, Prosper & Goncalves, Silvia & Meddahi, Nour, 2010. "Bootstrapping realized multivariate volatility measures," MPRA Paper 40123, University Library of Munich, Germany.
    11. Corsi, Fulvio & Peluso, Stefano & Audrino, Francesco, 2012. "Missing in Asynchronicity: A Kalman-EM Approach for Multivariate Realized Covariance Estimation," Economics Working Paper Series 1202, University of St. Gallen, School of Economics and Political Science.
    12. Iacopo Mastromatteo & Matteo Marsili & Patrick Zoi, 2010. "Financial correlations at ultra-high frequency: theoretical models and empirical estimation," Papers 1011.1011, arXiv.org, revised Feb 2011.
    13. 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.
    14. Nicolas Huth & Fr\'ed\'eric Abergel, 2011. "High Frequency Lead/lag Relationships - Empirical facts," Papers 1111.7103, arXiv.org, revised Jan 2012.

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