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Pre-Averaging Based Estimation of Quadratic Variation in the Presence of Noise and Jumps: Theory, Implementation, and Empirical Evidence

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  • Nikolaus Hautsch

    ()
    (Humboldt-Universität zu Berlin)

  • Mark Podolskij

    ()
    (ETH Zurich and CREATES)

Abstract

This paper provides theory as well as empirical results for pre-averaging estimators of the daily quadratic variation of asset prices. We derive jump robust inference for pre-averaging estimators, corresponding feasible central limit theorems and an explicit test on serial dependence in microstructure noise. Using transaction data of different stocks traded at the NYSE, we analyze the estimators’ sensitivity to the choice of the pre-averaging bandwidth and suggest an optimal interval length. Moreover, we investigate the dependence of pre-averaging based inference on the sampling scheme, the sampling frequency, microstructure noise properties as well as the occurrence of jumps. As a result of a detailed empirical study we provide guidance for optimal implementation of pre-averaging estimators and discuss potential pitfalls in practice.

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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 2010-29.

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Length: 53 Nikolaus Hautsch and Mark Podolskij
Date of creation: 01 Jul 2010
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Handle: RePEc:aah:create:2010-29

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

Related research

Keywords: Quadratic Variation; MarketMicrostructure Noise; Pre-averaging; Sampling Schemes; Jumps;

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References

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  1. 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, Oxford Financial Research Centre 2006fe05, Oxford Financial Research Centre.
  2. 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, Society for Financial Studies, vol. 18(2), pages 351-416.
  3. Oomen, Roel C.A., 2006. "Properties of Realized Variance Under Alternative Sampling Schemes," Journal of Business & Economic Statistics, American Statistical Association, American Statistical Association, vol. 24, pages 219-237, April.
  4. 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, American Statistical Association, vol. 96, pages 42-55, March.
  5. Hautsch, Nikolaus & Huang, Ruihong, 2012. "The market impact of a limit order," Journal of Economic Dynamics and Control, Elsevier, Elsevier, vol. 36(4), pages 501-522.
  6. 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, Royal Statistical Society, vol. 64(2), pages 253-280.
  7. 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, Economics Group, Nuffield College, University of Oxford 2004-W29, Economics Group, Nuffield College, University of Oxford.
  8. Vetter, Mathias & Podolskij, Mark, 2006. "Estimation of Volatility Functionals in the Simultaneous Presence of Microstructure Noise and Jumps," Technical Reports, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen 2006,51, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
  9. repec:oxf:wpaper:264 is not listed on IDEAS
  10. Jacod, Jean & Li, Yingying & Mykland, Per A. & Podolskij, Mark & Vetter, Mathias, 2007. "Microstructure noise in the continuous case: the pre-averaging approach," Technical Reports, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen 2007,41, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
  11. Hansen, Peter R. & Lunde, Asger, 2006. "Realized Variance and Market Microstructure Noise," Journal of Business & Economic Statistics, American Statistical Association, American Statistical Association, vol. 24, pages 127-161, April.
  12. Mark Podolskij & Mathias Vetter, 2008. "Bipower-type estimation in a noisy diffusion setting," CREATES Research Papers, School of Economics and Management, University of Aarhus 2008-25, School of Economics and Management, University of Aarhus.
  13. Jacod, Jean, 2008. "Asymptotic properties of realized power variations and related functionals of semimartingales," Stochastic Processes and their Applications, Elsevier, Elsevier, vol. 118(4), pages 517-559, April.
  14. Lan Zhang & Per A. Mykland & Yacine Ait-Sahalia, 2003. "A Tale of Two Time Scales: Determining Integrated Volatility with Noisy High Frequency Data," NBER Working Papers 10111, National Bureau of Economic Research, Inc.
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Citations

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Cited by:
  1. Hautsch, Nikolaus & Malec, Peter & Schienle, Melanie, 2011. "Capturing the zero: A new class of zero-augmented distributions and multiplicative error processes," CFS Working Paper Series, Center for Financial Studies (CFS) 2011/25, Center for Financial Studies (CFS).
  2. Maria Grith & Volker Krätschmer, 2010. "Parametric estimation of risk neutral density functions," SFB 649 Discussion Papers, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany SFB649DP2010-045, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  3. Szymon Borak & Adam Misiorek & Rafał Weron, 2010. "Models for Heavy-tailed Asset Returns," SFB 649 Discussion Papers, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany SFB649DP2010-049, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  4. Agnieszka Janek & Tino Kluge & Rafal Weron & Uwe Wystup, 2010. "FX Smile in the Heston Model," HSC Research Reports, Hugo Steinhaus Center, Wroclaw University of Technology HSC/10/02, Hugo Steinhaus Center, Wroclaw University of Technology.
  5. Nicole Wiebach & Lutz Hildebrandt, 2010. "Context Effects as Customer Reaction on Delisting of Brands," SFB 649 Discussion Papers, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany SFB649DP2010-056, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  6. Caporin, Massimiliano & Kolokolov, Aleksey & Renò, Roberto, 2014. "Multi-jumps," MPRA Paper 58175, University Library of Munich, Germany.
  7. Vladimir Panov, 2010. "Estimation of the signal subspace without estimation of the inverse covariance matrix," SFB 649 Discussion Papers, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany SFB649DP2010-050, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  8. Basteck, Christian & Daniëls, Tijmen R., 2011. "Every symmetric 3×3 global game of strategic complementarities has noise-independent selection," Journal of Mathematical Economics, Elsevier, vol. 47(6), pages 749-754.
  9. Enno Mammen & Christoph Rothe & Melanie Schienle, 2010. "Nonparametric Regression with Nonparametrically Generated Covariates," SFB 649 Discussion Papers, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany SFB649DP2010-059, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  10. Franziska Schulze, 2010. "Spatial Dependencies in German Matching Functions," SFB 649 Discussion Papers, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany SFB649DP2010-054, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  11. Ralf Sabiwalsky, 2010. "Executive Compensation Regulation and the Dynamics of the Pay-Performance Sensitivity," SFB 649 Discussion Papers, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany SFB649DP2010-051, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  12. Kris Boudt & Sébastien Laurent & Asger Lunde & Rogier Quaedvlieg, 2014. "Positive Semidefinite Integrated Covariance Estimation, Factorizations and Asynchronicity," CREATES Research Papers, School of Economics and Management, University of Aarhus 2014-05, School of Economics and Management, University of Aarhus.

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