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Efficient and feasible inference for the components of financial variation using blocked multipower variation

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Author Info

  • Per A. Mykland

    ()
    (Department of Statistics, University of Chicago, USA)

  • Neil Shephard

    ()
    (Nuffield College, Dept of Economics and Oxford-Man Institute of Quantitative Finance, University of Oxford.)

  • Kevin Sheppard

    ()
    (Dept of Economics and Oxford-Man Institute of Quantitative Finance, University of Oxford.)

Abstract

High frequency financial data allows us to learn more about volatility, volatility of volatility and jumps. One of the key techniques developed in the literature in recent years has been bipower variation and its multipower extension, which estimates time-varying volatility robustly to jumps. We improve the scope and efficiency of multipower variation by the use of a more sophisticated exploitation of high frequency data. This suggests very significant improvements in the power of jump tests. It also yields efficient estimates of the integrated variance of the continuous part of a semimartingale. The paper also shows how to extend the theory to the case where there is microstructure in the observations and derive the first nonparametric high frequency estimator of the volatility of volatility. A fundamental device in the paper is a new type of result showing path-by-path (strong) approximation between multipower and the (unobserved) RV based on the continuous part of the process.

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File URL: http://www.nuffield.ox.ac.uk/economics/papers/2012/mss120221.pdf
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Bibliographic Info

Paper provided by Economics Group, Nuffield College, University of Oxford in its series Economics Papers with number 2012-W02.

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Length: 44 pages
Date of creation: 21 Feb 2012
Date of revision:
Handle: RePEc:nuf:econwp:1202

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Web page: http://www.nuff.ox.ac.uk/economics/

Related research

Keywords: bipower variation; jumps; market microstructure noise; multipower variation; nonparametric analysis; quadratic variation; semimartingale; volatility; volatility of volatility.;

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References

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  1. Barndorff-Nielsen, Ole E. & Hansen, Peter Reinhard & Lunde, Asger & Shephard, Neil, 2011. "Multivariate realised kernels: Consistent positive semi-definite estimators of the covariation of equity prices with noise and non-synchronous trading," Journal of Econometrics, Elsevier, vol. 162(2), pages 149-169, June.
  2. 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.
  3. Kim Christensen & Roel Oomen & Mark Podolskij, 2010. "Realised quantile-based estimation of the integrated variance," Post-Print hal-00732538, HAL.
  4. Tim Bollerslev & Hao Zhou, 2007. "Expected Stock Returns and Variance Risk Premia," CREATES Research Papers 2007-17, School of Economics and Management, University of Aarhus.
  5. 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.
  6. 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.
  7. Torben G. Andersen & Dobrislav Dobrev & Ernst Schaumburg, 2010. "Jump-robust volatility estimation using nearest neighbor truncation," Staff Reports 465, Federal Reserve Bank of New York.
  8. Tim Bollerslev & Viktor Todorov, 2010. "Estimation of Jump Tails," CREATES Research Papers 2010-16, School of Economics and Management, University of Aarhus.
  9. Meddahi, Nour & Mykland, Per & Shephard, Neil, 2011. "Realized Volatility," Journal of Econometrics, Elsevier, vol. 160(1), pages 1-1, January.
  10. Torben G. Andersen & Dobrislav Dobrev & Ernst Schaumburg, 2011. "A Functional Filtering and Neighborhood Truncation Approach to Integrated Quarticity Estimation," CREATES Research Papers 2011-23, School of Economics and Management, University of Aarhus.
  11. Per A. Mykland & Lan Zhang, 2009. "Inference for Continuous Semimartingales Observed at High Frequency," Econometrica, Econometric Society, vol. 77(5), pages 1403-1445, 09.
  12. 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.
  13. Christensen, Kim & Podolskij, Mark, 2006. "Range-Based Estimation of Quadratic Variation," Technical Reports 2006,37, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
  14. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold, 2007. "Roughing It Up: Including Jump Components in the Measurement, Modeling, and Forecasting of Return Volatility," The Review of Economics and Statistics, MIT Press, vol. 89(4), pages 701-720, November.
  15. Martens, Martin & van Dijk, Dick, 2007. "Measuring volatility with the realized range," Journal of Econometrics, Elsevier, vol. 138(1), pages 181-207, May.
  16. 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.
  17. F. M. Bandi & J. R. Russell, 2008. "Microstructure Noise, Realized Variance, and Optimal Sampling," Review of Economic Studies, Oxford University Press, vol. 75(2), pages 339-369.
  18. Christensen, Kim & Podolski, Mark, 2005. "Asymptotic theory for range-based estimation of integrated variance of a continuous semi-martingale," Technical Reports 2005,18, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
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Cited by:
  1. Markus Bibinger & Per A. Mykland, 2013. "Inference for Multi-Dimensional High-Frequency Data: Equivalence of Methods, Central Limit Theorems, and an Application to Conditional Independence Testing," SFB 649 Discussion Papers SFB649DP2013-006, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.

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