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Bipower-type estimation in a noisy diffusion setting

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  • Mark Podolskij
  • Mathias Vetter

    ()
    (School of Economics and Management, University of Aarhus, Denmark and CREATES)

Abstract

We consider a new class of estimators for volatility functionals in the setting of frequently observed Itô diffusions which are disturbed by i.i.d. noise. These statistics extend the approach of pre-averaging as a general method for the estimation of the integrated volatility in the presence of microstructure noise and are closely related to the original concept of bipower variation in the no-noise case. We show that this approach provides efficient estimators for a large class of integrated powers of volatility and prove the associated (stable) central limit theorems. In a more general Itô semimartingale framework this method can be used to define both estimators for the entire quadratic variation of the underlying process and jump-robust estimators which are consistent for various functionals of volatility. As a by-product we obtain a simple test for the presence of jumps in the underlying semimartingale.

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Bibliographic Info

Paper provided by School of Economics and Management, University of Aarhus in its series CREATES Research Papers with number 2008-25.

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Length: 42
Date of creation: 26 May 2008
Date of revision:
Handle: RePEc:aah:create:2008-25

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Web page: http://www.econ.au.dk/afn/

Related research

Keywords: Bipower Variation; Central Limit Theorem; High-Frequency Data; Microstructure Noise; Quadratic Variation; Semimartingale Theory; Test for Jumps;

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References

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  1. Jean Jacod & Yingying Li & Per A. Mykland & Mark Podolskij & Mathias Vetter, 2007. "Microstructure Noise in the Continuous Case: The Pre-Averaging Approach - JLMPV-9," CREATES Research Papers 2007-43, School of Economics and Management, University of Aarhus.
  2. Ole Barndorff-Nielsen & Svend Erik Graversen & Jean Jacod & Mark Podolskij & Neil Shephard, 2004. "A Central Limit Theorem for Realised Power and Bipower Variations of Continuous Semimartingales," Economics Papers 2004-W29, Economics Group, Nuffield College, University of Oxford.
  3. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
  4. 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.
  5. 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.
  6. 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.
  7. Ole E. Barndorff-Nielsen, 2004. "Power and Bipower Variation with Stochastic Volatility and Jumps," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 2(1), pages 1-37.
  8. 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.
  9. 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.
  10. Neil Shephard & Ole E. Barndorff-Nielsen, 2003. "Power and bipower variation with stochastic volatility and jumps," Economics Series Working Papers 2003-W18, University of Oxford, Department of Economics.
  11. Mark Podolskij & Mathias Vetter, 2007. "Estimation of Volatility Functionals in the Simultaneous Presence of Microstructure Noise and Jumps," CREATES Research Papers 2007-27, School of Economics and Management, University of Aarhus.
  12. Chan, K C, et al, 1992. " An Empirical Comparison of Alternative Models of the Short-Term Interest Rate," Journal of Finance, American Finance Association, vol. 47(3), pages 1209-27, July.
  13. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-54, May-June.
  14. Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1980. " An Analysis of Variable Rate Loan Contracts," Journal of Finance, American Finance Association, vol. 35(2), pages 389-403, May.
  15. 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.
  16. Vasicek, Oldrich Alfonso, 1977. "Abstract: An Equilibrium Characterization of the Term Structure," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 12(04), pages 627-627, November.
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Citations

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Cited by:
  1. Nikolaus Hautsch & Mark Podolskij, 2010. "Pre-Averaging Based Estimation of Quadratic Variation in the Presence of Noise and Jumps: Theory, Implementation, and Empirical Evidence," CREATES Research Papers 2010-29, School of Economics and Management, University of Aarhus.
  2. Valentina Corradi & Norman Swanson & Walter Distaso, 2006. "Predictive Inference for Integrated Volatility," Departmental Working Papers 200616, Rutgers University, Department of Economics.
  3. Jean Jacod & Mark Podolskij & Mathias Vetter, 2008. "Intertemporal Asset Allocation with Habit Formation in Preferences: An Approximate Analytical Solution," CREATES Research Papers 2008-61, School of Economics and Management, University of Aarhus.
  4. M. Podolskij & D. Ziggel, 2010. "New tests for jumps in semimartingale models," Statistical Inference for Stochastic Processes, Springer, vol. 13(1), pages 15-41, April.
  5. Christensen, Kim & Podolskij, Mark & Vetter, Mathias, 2013. "On covariation estimation for multivariate continuous Itô semimartingales with noise in non-synchronous observation schemes," Journal of Multivariate Analysis, Elsevier, vol. 120(C), pages 59-84.

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