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Bootstrapping realized multivariate volatility measures

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

Abstract

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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Bibliographic Info

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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Keywords: Realized regression; realized beta; realized correlation; bootstrap; Edgeworth expansions;

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References

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  1. 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.
  2. 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.
  3. 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, Oxford Financial Research Centre 2006fe05, Oxford Financial Research Centre.
  4. MEDDAHI, Nour, 2001. "A Theoretical Comparison Between Integrated and Realized Volatilies," Cahiers de recherche, Universite de Montreal, Departement de sciences economiques 2001-26, Universite de Montreal, Departement de sciences economiques.
  5. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Paul Labys, 2003. "Modeling and Forecasting Realized Volatility," Econometrica, Econometric Society, Econometric Society, vol. 71(2), pages 579-625, March.
  6. Ole E. Barndorff-Nielsen & Shephard, 2002. "Econometric analysis of realized volatility and its use in estimating stochastic volatility models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, Royal Statistical Society, vol. 64(2), pages 253-280.
  7. Ole E. Barndorff-Nielsen & Neil Shephard, 2003. "Econometrics of testing for jumps in financial economics using bipower variation," Economics Papers 2003-W21, Economics Group, Nuffield College, University of Oxford.
  8. Zhang, Lan & Mykland, Per A. & Aït-Sahalia, Yacine, 2011. "Edgeworth expansions for realized volatility and related estimators," Journal of Econometrics, Elsevier, Elsevier, vol. 160(1), pages 190-203, January.
  9. Neil Shephard, 2005. "Limit theorems for bipower variation in financial econometrics," Economics Series Working Papers, University of Oxford, Department of Economics 2005-FE-09, University of Oxford, Department of Economics.
  10. Per Mykland, 2012. "A Gaussian calculus for inference from high frequency data," Annals of Finance, Springer, Springer, vol. 8(2), pages 235-258, May.
  11. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Jin (Ginger) Wu, 2005. "A Framework for Exploring the Macroeconomic Determinants of Systematic Risk," NBER Working Papers 11134, National Bureau of Economic Research, Inc.
  12. Neil Shephard & Ole E. Barndorff-Nielsen & Peter Reinhard Hansen, 2008. "Multivariate realised kernels: consistent positive semi-definite estimators of the covariation of equity prices with noise and non-synchronous trading," Economics Series Working Papers, University of Oxford, Department of Economics 397, University of Oxford, Department of Economics.
  13. 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.
  14. 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.
  15. 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, Econometric Society, vol. 72(3), pages 885-925, 05.
  16. Zhang, Lan, 2011. "Estimating covariation: Epps effect, microstructure noise," Journal of Econometrics, Elsevier, Elsevier, vol. 160(1), pages 33-47, January.
  17. Sílvia Gonçalves & Nour Meddahi, 2009. "Bootstrapping Realized Volatility," Econometrica, Econometric Society, Econometric Society, vol. 77(1), pages 283-306, 01.
  18. Silvia Goncalves & Nour Meddahi, 2008. "Edgeworth Corrections for Realized Volatility," Econometric Reviews, Taylor & Francis Journals, Taylor & Francis Journals, vol. 27(1-3), pages 139-162.
  19. Viceira, Luis M., 2012. "Bond risk, bond return volatility, and the term structure of interest rates," International Journal of Forecasting, Elsevier, Elsevier, vol. 28(1), pages 97-117.
  20. Per Aslak Mykland & Lan Zhang, 2006. "ANOVA for diffusions and It\^{o} processes," Papers math/0611274, arXiv.org.
  21. 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.
  22. 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, 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. Peter Reinhard Hansen & Asger Lunde & Valeri Voev, 2012. "Realized Beta GARCH: A Multivariate GARCH Model with Realized Measures of Volatility and Covolatility," Global COE Hi-Stat Discussion Paper Series, Institute of Economic Research, Hitotsubashi University gd12-269, Institute of Economic Research, Hitotsubashi University.
  2. Hwang, Eunju & Shin, Dong Wan, 2013. "Stationary bootstrapping realized volatility," Statistics & Probability Letters, Elsevier, Elsevier, vol. 83(9), pages 2045-2051.
  3. Andrew J. Patton & Michela Verardo, 2009. "Does beta move with news?: Systematic risk and firm-specific information flows," LSE Research Online Documents on Economics, London School of Economics and Political Science, LSE Library 24421, London School of Economics and Political Science, LSE Library.
  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," Economics Papers 2008-W10, Economics Group, Nuffield College, University of Oxford.
  5. BAUWENS, Luc & STORTI, Giuseppe, 2012. "Computationally efficient inference procedures for vast dimensional realized covariance models," CORE Discussion Papers, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) 2012028, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  6. Vincenzo Candila, 2013. "A Comparison Of The Forecasting Performances Of Multivariate Volatility Models," Working Papers, Dipartimento di Scienze Economiche e Statistiche, Università degli Studi di Salerno 3_228, Dipartimento di Scienze Economiche e Statistiche, Università degli Studi di Salerno.
  7. Ulrich Hounyo, 2013. "Bootstrapping realized volatility and realized beta under a local Gaussianity assumption," CREATES Research Papers 2013-30, School of Economics and Management, University of Aarhus.
  8. Diego Fresoli & Esther Ruiz, 2014. "The uncertainty of conditional returns, volatilities and correlations in DCC models," Statistics and Econometrics Working Papers, Universidad Carlos III, Departamento de Estadística y Econometría ws140202, Universidad Carlos III, Departamento de Estadística y Econometría.

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