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A blocking and regularization approach to high dimensional realized covariance estimation

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  • Nikolaus Hautsch
  • Lada M. Kyj
  • Roel C.A. Oomen

Abstract

We introduce a regularization and blocking estimator for well-conditioned high-dimensional daily covariances using high-frequency data. Using the Barndorff-Nielsen, Hansen, Lunde, and Shephard (2008a) kernel estimator, we estimate the covariance matrix block-wise and regularize it. A data-driven grouping of assets of similar trading frequency ensures the reduction of data loss due to refresh time sampling. In an extensive simulation study mimicking the empirical features of the S&P 1500 universe we show that the ’RnB’ estimator yields efficiency gains and outperforms competing kernel estimators for varying liquidity settings, noise-to-signal ratios, and dimensions. An empirical application of forecasting daily covariances of the S&P 500 index confirms the simulation results.

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Bibliographic Info

Paper provided by Sonderforschungsbereich 649, Humboldt University, Berlin, Germany in its series SFB 649 Discussion Papers with number SFB649DP2009-049.

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Length: 34 pages
Date of creation: Oct 2009
Date of revision:
Handle: RePEc:hum:wpaper:sfb649dp2009-049

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Keywords: covariance estimation; blocking; realized kernel; regularization; microstructure; asynchronous trading;

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References

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  1. Alexei Onatski, 2009. "Testing Hypotheses About the Number of Factors in Large Factor Models," Econometrica, Econometric Society, Econometric Society, vol. 77(5), pages 1447-1479, 09.
  2. Bonato, Matteo & Caporin, Massimiliano & Ranaldo, Angelo, 2012. "Forecasting Realized (Co)Variances with a Bloc Structure Wishart Autoregressive Model," Working Papers on Finance 1211, University of St. Gallen, School of Finance.
  3. Gilles Zumbach, 2009. "The empirical properties of large covariance matrices," Papers 0903.1525, arXiv.org.
  4. Bandi, Federico M. & Russell, Jeffrey R., 2006. "Separating microstructure noise from volatility," Journal of Financial Economics, Elsevier, Elsevier, vol. 79(3), pages 655-692, March.
  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, American Statistical Association, vol. 100, pages 1394-1411, December.
  6. Olivier Ledoit & Michael Wolf, 2001. "Improved estimation of the covariance matrix of stock returns with an application to portofolio selection," Economics Working Papers, Department of Economics and Business, Universitat Pompeu Fabra 586, Department of Economics and Business, Universitat Pompeu Fabra.
  7. Torben G. Andersen & Tim Bollerslev & Per Houmann Frederiksen & Morten Ørregaard Nielsen, 2007. "Continuous-Time Models, Realized Volatilities, and Testable Distributional Implications for Daily Stock Returns," CREATES Research Papers 2007-21, School of Economics and Management, University of Aarhus.
  8. Griffin, Jim E. & Oomen, Roel C.A., 2011. "Covariance measurement in the presence of non-synchronous trading and market microstructure noise," Journal of Econometrics, Elsevier, Elsevier, vol. 160(1), pages 58-68, January.
  9. 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.
  10. 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.
  11. deB. Harris, Frederick H. & McInish, Thomas H. & Shoesmith, Gary L. & Wood, Robert A., 1995. "Cointegration, Error Correction, and Price Discovery on Informationally Linked Security Markets," Journal of Financial and Quantitative Analysis, Cambridge University Press, Cambridge University Press, vol. 30(04), pages 563-579, December.
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  13. Ravi Jagannathan & Tongshu Ma, 2002. "Risk Reduction in Large Portfolios: Why Imposing the Wrong Constraints Helps," NBER Working Papers 8922, National Bureau of Economic Research, Inc.
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Citations

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Cited by:
  1. 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.
  2. Matthias R. Fengler & Ostap Okhrin, 2012. "Realized Copula," SFB 649 Discussion Papers SFB649DP2012-034, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  3. 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.
  4. Manabu Asai & Michael McAleer, 2014. "Forecasting Co-Volatilities via Factor Models with Asymmetry and Long Memory in Realized Covariance," Tinbergen Institute Discussion Papers 14-037/III, Tinbergen Institute.
  5. Manabu Asai & Michael McAleer, 2014. "Forecasting Co-Volatilities via Factor Models with Asymmetry and Long Memory in Realized Covariance," Working Papers in Economics, University of Canterbury, Department of Economics and Finance 14/10, University of Canterbury, Department of Economics and Finance.
  6. Torben G. Andersen & Tim Bollerslev & Peter F. Christoffersen & Francis X. Diebold, 2011. "Financial Risk Measurement for Financial Risk Management," CREATES Research Papers 2011-37, School of Economics and Management, University of Aarhus.
  7. Griffin, Jim E. & Oomen, Roel C.A., 2011. "Covariance measurement in the presence of non-synchronous trading and market microstructure noise," Journal of Econometrics, Elsevier, Elsevier, vol. 160(1), pages 58-68, January.
  8. 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.
  9. Matteo Luciani & David Veredas, 2012. "A model for vast panels of volatilities," Banco de Espa�a Working Papers 1230, Banco de Espa�a.

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