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Edgeworth Expansions for Realized Volatility and Related Estimators

  • Lan Zhang
  • Per A. Mykland
  • Yacine Ait-Sahalia

This paper shows that the asymptotic normal approximation is often insufficiently accurate for volatility estimators based on high frequency data. To remedy this, we compute Edgeworth expansions for such estimators. Unlike the usual expansions, we have found that in order to obtain meaningful terms, one needs to let the size of the noise to go zero asymptotically. The results have application to Cornish-Fisher inversion and bootstrapping.

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File URL: http://www.nber.org/papers/t0319.pdf
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Paper provided by National Bureau of Economic Research, Inc in its series NBER Technical Working Papers with number 0319.

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Date of creation: Oct 2005
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Handle: RePEc:nbr:nberte:0319
Note: TWP
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  1. 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, vol. 64(2), pages 253-280.
  2. Ole E. Barndorff-Nielsen & Peter R. Hansen & Asger Lunde & Neil Shephard, 2006. "Subsampling realised kernels," OFRC Working Papers Series 2006fe06, Oxford Financial Research Centre.
  3. Offer Lieberman & Peter C. B. Phillips, 2006. "Refined Inference on Long Memory in Realized Volatility," Cowles Foundation Discussion Papers 1549, Cowles Foundation for Research in Economics, Yale University.
  4. Ole E. Barndorff-Nielsen & Peter Reinhard Hansen & Asger Lunde & Neil Shephard, 2004. "Regular and Modified Kernel-Based Estimators of Integrated Variance: The Case with Independent Noise," OFRC Working Papers Series 2004fe20, Oxford Financial Research Centre.
  5. Asger Lunde & Peter Reinhard Hansen, 2004. "Realized Variance and IID Market Microstructure Noise," Econometric Society 2004 North American Summer Meetings 526, Econometric Society.
  6. Jacod, Jean & Li, Yingying & Mykland, Per A. & Podolskij, Mark & Vetter, Mathias, 2009. "Microstructure noise in the continuous case: The pre-averaging approach," Stochastic Processes and their Applications, Elsevier, vol. 119(7), pages 2249-2276, July.
  7. Meddahi, N., 2001. "A Theoretical Comparison Between Integrated and Realized Volatilies," Cahiers de recherche 2001-26, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  8. Silvia Goncalves & Nour Meddahi, 2008. "Edgeworth Corrections for Realized Volatility," Econometric Reviews, Taylor & Francis Journals, vol. 27(1-3), pages 139-162.
  9. Yacine Aït-Sahalia, 2005. "How Often to Sample a Continuous-Time Process in the Presence of Market Microstructure Noise," Review of Financial Studies, Society for Financial Studies, vol. 18(2), pages 351-416.
  10. Zhou, Bin, 1996. "High-Frequency Data and Volatility in Foreign-Exchange Rates," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(1), pages 45-52, January.
  11. Sílvia Gonçalves & Nour Meddahi, 2009. "Bootstrapping Realized Volatility," Econometrica, Econometric Society, vol. 77(1), pages 283-306, 01.
  12. 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 2006fe05, Oxford Financial Research Centre.
  13. Bollerslev, Tim & Zhou, Hao, 2002. "Estimating stochastic volatility diffusion using conditional moments of integrated volatility," Journal of Econometrics, Elsevier, vol. 109(1), pages 33-65, July.
  14. Kadane, Joseph B, 1971. "Comparison of k-Class Estimators when the Disturbances are Small," Econometrica, Econometric Society, vol. 39(5), pages 723-37, September.
  15. 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.
  16. David Brillinger, 1969. "The calculation of cumulants via conditioning," Annals of the Institute of Statistical Mathematics, Springer, vol. 21(1), pages 215-218, December.
  17. Andersen, Torben G. & Bollerslev, Tim & Diebold, Francis X. & Ebens, Heiko, 2001. "The distribution of realized stock return volatility," Journal of Financial Economics, Elsevier, vol. 61(1), pages 43-76, July.
  18. Hansen, Peter R. & Lunde, Asger, 2006. "Realized Variance and Market Microstructure Noise," Journal of Business & Economic Statistics, American Statistical Association, vol. 24, pages 127-161, April.
  19. 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.
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