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Bootstrapping realized multivariate volatility measures

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Author Info

  • Dovonon, Prosper
  • Gonçalves, Sílvia
  • Meddahi, Nour

Abstract

We propose a bootstrap method for statistics that are a function of multivariate high frequency returns such as realized regression, covariance and correlation coefficients. 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 error heteroskedasticity, the Edgeworth expansion for the pairs 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

Article provided by Elsevier in its journal Journal of Econometrics.

Volume (Year): 172 (2013)
Issue (Month): 1 ()
Pages: 49-65

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Handle: RePEc:eee:econom:v:172:y:2013:i:1:p:49-65

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

Related research

Keywords: Realized regression; Realized beta; Realized correlation; Bootstrap; Edgeworth expansions;

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References

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  1. 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.
  2. 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.
  3. Andersen, Torben G. & Bollerslev, Tim & Diebold, Francis X. & Wu, Jin, 2005. "A framework for exploring the macroeconomic determinants of systematic risk," CFS Working Paper Series 2005/04, Center for Financial Studies (CFS).
  4. 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.
  5. 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," OFRC Working Papers Series 2008fe29, Oxford Financial Research Centre.
  6. Ole E. Barndorff-Nielsen & Sven Erik Graversen & Jean Jacod & Neil Shephard, 2005. "Limit theorems for bipower variation in financial econometrics," Economics Papers 2005-W06, Economics Group, Nuffield College, University of Oxford.
  7. Per Mykland, 2012. "A Gaussian calculus for inference from high frequency data," Annals of Finance, Springer, vol. 8(2), pages 235-258, May.
  8. Mark Podolskij & Mathias Vetter, 2010. "Understanding limit theorems for semimartingales: a short survey," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 64(s1), pages 329-351.
  9. 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.
  10. Per Aslak Mykland & Lan Zhang, 2006. "ANOVA for diffusions and It\^{o} processes," Papers math/0611274, arXiv.org.
  11. MEDDAHI, Nour, 2001. "A Theoretical Comparison Between Integrated and Realized Volatilies," Cahiers de recherche 2001-26, Universite de Montreal, Departement de sciences economiques.
  12. 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.
  13. 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.
  14. Sílvia Gonçalves & Nour Meddahi, 2009. "Bootstrapping Realized Volatility," Econometrica, Econometric Society, vol. 77(1), pages 283-306, 01.
  15. 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.
  16. 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.
  17. Silvia Goncalves & Nour Meddahi, 2008. "Edgeworth Corrections for Realized Volatility," Econometric Reviews, Taylor & Francis Journals, vol. 27(1-3), pages 139-162.
  18. 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.
  19. Lan Zhang & Per A. Mykland & Yacine Ait-Sahalia, 2005. "Edgeworth Expansions for Realized Volatility and Related Estimators," NBER Technical Working Papers 0319, National Bureau of Economic Research, Inc.
  20. 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.
  21. Zhang, Lan, 2011. "Estimating covariation: Epps effect, microstructure noise," Journal of Econometrics, Elsevier, vol. 160(1), pages 33-47, January.
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Citations

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Cited by:
  1. 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.
  2. Vincenzo Candila, 2013. "A Comparison Of The Forecasting Performances Of Multivariate Volatility Models," Working Papers 3_228, Dipartimento di Scienze Economiche e Statistiche, Università degli Studi di Salerno.
  3. Diego Fresoli & Esther Ruiz, 2014. "The uncertainty of conditional returns, volatilities and correlations in DCC models," Statistics and Econometrics Working Papers ws140202, Universidad Carlos III, Departamento de Estadística y Econometría.
  4. BAUWENS, Luc & STORTI, Giuseppe, 2012. "Computationally efficient inference procedures for vast dimensional realized covariance models," CORE Discussion Papers 2012028, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  5. 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.
  6. 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.
  7. Hwang, Eunju & Shin, Dong Wan, 2013. "Stationary bootstrapping realized volatility," Statistics & Probability Letters, Elsevier, vol. 83(9), pages 2045-2051.

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