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How precise is the finite sample approximation of the asymptotic distribution of realised variation measures in the presence of jumps?

  • Almut E. D. Veraart

    ()

    (CREATES, School of Economics and Management Aarhus University)

This paper studies the impact of jumps on volatility estimation and inference based on various realised variation measures such as realised variance, realised multipower variation and truncated realised multipower variation. We review the asymptotic theory of those realised variation measures and present a new estimator for the asymptotic ‘variance’ of the centered realised variance in the presence of jumps. Next, we compare the finite sample performance of the various estimators by means of detailed Monte Carlo studies where we study the impact of the jump activity, the jump size of the jumps in the price and the presence of additional independent or dependent jumps in the volatility on the finite sample performance of the various estimators. We find that the finite sample performance of realised variance, and in particular of the log–transformed realised variance, is generally good, whereas the jump–robust statistics turn out not to be as jump robust as the asymptotic theory would suggest in the presence of a highly active jump process. In an empirical study on high frequency data from the Standard & Poor’s Depository Receipt (SPY), we investigate the impact of jumps on inference on volatility by realised variance in practice.

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Paper provided by School of Economics and Management, University of Aarhus in its series CREATES Research Papers with number 2010-65.

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Date of creation: 18 Sep 2010
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Handle: RePEc:aah:create:2010-65
Contact details of provider: Web page: http://www.econ.au.dk/afn/

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  1. Kim Christensen & Roel Oomen & Mark Podolskij, 2011. "Fact or friction: Jumps at ultra high frequency," CREATES Research Papers 2011-19, School of Economics and Management, University of Aarhus.
  2. Veraart, Almut E.D., 2010. "Inference For The Jump Part Of Quadratic Variation Of Itô Semimartingales," Econometric Theory, Cambridge University Press, vol. 26(02), pages 331-368, April.
  3. Xin Huang & George Tauchen, 2005. "The Relative Contribution of Jumps to Total Price Variance," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 3(4), pages 456-499.
  4. Holger Dette & Mark Podolskij & Mathias Vetter, 2006. "Estimation of Integrated Volatility in Continuous-Time Financial Models with Applications to Goodness-of-Fit Testing," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 33(2), pages 259-278.
  5. Neil Shephard & Ole Barndorff-Nielsen, 2003. "Econometrics of testing for jumps in financial economics using bipower variation," Economics Series Working Papers 2004-FE-01, University of Oxford, Department of Economics.
  6. 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.
  7. Kristensen, Dennis, 2010. "Nonparametric Filtering Of The Realized Spot Volatility: A Kernel-Based Approach," Econometric Theory, Cambridge University Press, vol. 26(01), pages 60-93, February.
  8. Ole E. Barndorff-Nielsen & Peter Reinhard Hansen & Asger Lunde & Neil Shephard, 2008. "Designing Realized Kernels to Measure the ex post Variation of Equity Prices in the Presence of Noise," Econometrica, Econometric Society, vol. 76(6), pages 1481-1536, November.
  9. Corsi, Fulvio & Pirino, Davide & Renò, Roberto, 2010. "Threshold bipower variation and the impact of jumps on volatility forecasting," Journal of Econometrics, Elsevier, vol. 159(2), pages 276-288, December.
  10. Jean Jacod & Viktor Todorov, 2010. "Do price and volatility jump together?," Papers 1010.4990, arXiv.org.
  11. Hiroyuki Kawakatsu, 2007. "Numerical integration-based Gaussian mixture filters for maximum likelihood estimation of asymmetric stochastic volatility models," Econometrics Journal, Royal Economic Society, vol. 10(2), pages 342-358, 07.
  12. Cecilia Mancini, 2009. "Non-parametric Threshold Estimation for Models with Stochastic Diffusion Coefficient and Jumps," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 36(2), pages 270-296.
  13. Almut E. D. Veraart & Luitgard A. M. Veraart, 2009. "Stochastic volatility and stochastic leverage," CREATES Research Papers 2009-20, School of Economics and Management, University of Aarhus.
  14. Vetter, Mathias, 2010. "Limit theorems for bipower variation of semimartingales," Stochastic Processes and their Applications, Elsevier, vol. 120(1), pages 22-38, January.
  15. Dean P. Foster & Daniel B. Nelson, 1994. "Continuous Record Asymptotics for Rolling Sample Variance Estimators," NBER Technical Working Papers 0163, National Bureau of Economic Research, Inc.
  16. Suzanne S. Lee & Per A. Mykland, 2008. "Jumps in Financial Markets: A New Nonparametric Test and Jump Dynamics," Review of Financial Studies, Society for Financial Studies, vol. 21(6), pages 2535-2563, November.
  17. Jacod, Jean, 2008. "Asymptotic properties of realized power variations and related functionals of semimartingales," Stochastic Processes and their Applications, Elsevier, vol. 118(4), pages 517-559, April.
  18. Ai[diaeresis]t-Sahalia, Yacine & Kimmel, Robert, 2007. "Maximum likelihood estimation of stochastic volatility models," Journal of Financial Economics, Elsevier, vol. 83(2), pages 413-452, February.
  19. 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.
  20. Vetter, Mathias & Podolskij, Mark, 2006. "Estimation of Volatility Functionals in the Simultaneous Presence of Microstructure Noise and Jumps," Technical Reports 2006,51, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
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