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Bootstrapping realized multivariate volatility measures

  • Dovonon, Prosper
  • Goncalves, Silvia
  • Meddahi, Nour

We study bootstrap methods for statistics that are a function of multivariate high frequency returns such as realized regression coefficients and realized covariances and correlations. For these measures of covariation, the Monte Carlo simulation results of Barndorff-Nielsen and Shephard (2004) show that finite sample distortions associated with their feasible asymptotic theory approach may arise if sampling is not too frequent. This motivates our use of the bootstrap as an alternative tool of inference for covariation measures. We consider an i.i.d. bootstrap applied to the vector of returns. We show that the finite sample performance of the bootstrap is superior to the existing first-order asymptotic theory. Nevertheless, and contrary to the existing results in the bootstrap literature for regression models subject to heteroskedasticity in the error term, the Edgeworth expansion for the i.i.d. bootstrap that we develop here shows that this method is not second order accurate. We argue that this is due to the fact that the conditional mean parameters of realized regression models are heterogeneous under stochastic volatility.

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Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 40123.

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Date of creation: Jul 2010
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Handle: RePEc:pra:mprapa:40123
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  1. 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.
  2. Ole E. Barndorff-Nielsen & Peter Reinhard Hansen & Asger Lunde & Neil Shephard, 2011. "Multivariate realised kernels: Consistent positive semi-definite estimators of the covariation of equity prices with noise and non-synchronous trading," Post-Print hal-00815564, HAL.
  3. Ole E. Barndorff-Nielsen & Neil Shephard, 2004. "Econometrics of testing for jumps in financial economics using bipower variation ," OFRC Working Papers Series 2004fe01, Oxford Financial Research Centre.
  4. Per Mykland, 2012. "A Gaussian calculus for inference from high frequency data," Annals of Finance, Springer, vol. 8(2), pages 235-258, May.
  5. Zhang, Lan, 2011. "Estimating covariation: Epps effect, microstructure noise," Journal of Econometrics, Elsevier, vol. 160(1), pages 33-47, January.
  6. Viceira, Luis M., 2012. "Bond risk, bond return volatility, and the term structure of interest rates," International Journal of Forecasting, Elsevier, vol. 28(1), pages 97-117.
  7. Barndorff-Nielsen, Ole E. & Graversen, Svend Erik & Jacod, Jean & Shephard, Neil, 2006. "Limit Theorems For Bipower Variation In Financial Econometrics," Econometric Theory, Cambridge University Press, vol. 22(04), pages 677-719, August.
  8. Ole E. Barndorff-Nielsen & Neil Shephard, 2004. "Econometric Analysis of Realized Covariation: High Frequency Based Covariance, Regression, and Correlation in Financial Economics," Econometrica, Econometric Society, vol. 72(3), pages 885-925, 05.
  9. 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.
  10. Anderson, Torben G. & Bollerslev, Tim & Diebold, Francis X. & Labys, Paul, 2002. "Modeling and Forecasting Realized Volatility," Working Papers 02-12, Duke University, Department of Economics.
  11. Nour Meddahi, 2002. "A theoretical comparison between integrated and realized volatility," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 17(5), pages 479-508.
  12. Mark Podolskij & Mathias Vetter, 2009. "Understanding limit theorems for semimartingales: a short survey," CREATES Research Papers 2009-47, School of Economics and Management, University of Aarhus.
  13. Per Aslak Mykland & Lan Zhang, 2006. "ANOVA for diffusions and It\^{o} processes," Papers math/0611274,
  14. Silvia Goncalves & Nour Meddahi, 2008. "Edgeworth Corrections for Realized Volatility," Econometric Reviews, Taylor & Francis Journals, vol. 27(1-3), pages 139-162.
  15. Neil Shephard & Ole E. Barndorff-Nielsen, 2006. "Designing realised kernels to measure the ex-post variation of equity prices in the presence of noise," Economics Series Working Papers 2006-W03, University of Oxford, Department of Economics.
  16. 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.
  17. 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.
  18. 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.
  19. Viktor Todorov & Tim Bollerslev, 2007. "Jumps and Betas: A New Framework for Disentangling and Estimating Systematic Risks," CREATES Research Papers 2007-15, School of Economics and Management, University of Aarhus.
  20. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Jin (Ginger) Wu, 2005. "A Framework for Exploring the Macroeconomic Determinants of Systematic Risk," PIER Working Paper Archive 05-009, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
  21. Sílvia Gonçalves & Nour Meddahi, 2009. "Bootstrapping Realized Volatility," Econometrica, Econometric Society, vol. 77(1), pages 283-306, 01.
  22. 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, vol. 160(1), pages 58-68, January.
  23. Ole E. Barndorff-Nielsen & Peter Reinhard Hansen & Asger Lunde & Neil Shephard, 2011. "Multivariate realised kernels: Consistent positive semi-definite estimators of the covariation of equity prices with noise and non-synchronous trading," Post-Print peer-00815564, HAL.
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