IDEAS home Printed from https://ideas.repec.org/p/nbr/nberwo/11380.html
   My bibliography  Save this paper

Ultra High Frequency Volatility Estimation with Dependent Microstructure Noise

Author

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

Abstract

We analyze the impact of time series dependence in market microstructure noise on the properties of estimators of the integrated volatility of an asset price based on data sampled at frequencies high enough for that noise to be a dominant consideration. We show that combining two time scales for that purpose will work even when the noise exhibits time series dependence, analyze in that context a refinement of this approach based on multiple time scales, and compare empirically our different estimators to the standard realized volatility.

Suggested Citation

  • Yacine Ait-Sahalia & Per A. Mykland & Lan Zhang, 2005. "Ultra High Frequency Volatility Estimation with Dependent Microstructure Noise," NBER Working Papers 11380, National Bureau of Economic Research, Inc.
  • Handle: RePEc:nbr:nberwo:11380
    Note: AP
    as

    Download full text from publisher

    File URL: http://www.nber.org/papers/w11380.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Fulvio Corsi & Stefan Mittnik & Christian Pigorsch & Uta Pigorsch, 2008. "The Volatility of Realized Volatility," Econometric Reviews, Taylor & Francis Journals, vol. 27(1-3), pages 46-78.
    2. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Paul Labys, 1999. "The Distribution of Exchange Rate Volatility," New York University, Leonard N. Stern School Finance Department Working Paper Seires 99-059, New York University, Leonard N. Stern School of Business-.
    3. 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.
    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. Zhang, Lan, 2011. "Estimating covariation: Epps effect, microstructure noise," Journal of Econometrics, Elsevier, vol. 160(1), pages 33-47, January.
    6. Yacine Ait--Sahalia & Per A. Mykland, 2003. "The Effects of Random and Discrete Sampling when Estimating Continuous--Time Diffusions," Econometrica, Econometric Society, vol. 71(2), pages 483-549, March.
    7. Ramazan GenÁay & Giuseppe Ballocchi & Michel Dacorogna & Richard Olsen & Olivier Pictet, 2002. "Real-Time Trading Models and the Statistical Properties of Foreign Exchange Rates," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 43(2), pages 463-492, May.
    8. Yacine Aït-Sahalia, 2005. "How Often to Sample a Continuous-Time Process in the Presence of Market Microstructure Noise," The Review of Financial Studies, Society for Financial Studies, vol. 18(2), pages 351-416.
    9. Sílvia Gonçalves & Nour Meddahi, 2009. "Bootstrapping Realized Volatility," Econometrica, Econometric Society, vol. 77(1), pages 283-306, January.
    10. Choi, J. Y. & Salandro, Dan & Shastri, Kuldeep, 1988. "On the Estimation of Bid-Ask Spreads: Theory and Evidence," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 23(2), pages 219-230, June.
    11. 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.
    12. Ole E. Barndorff‐Nielsen & Neil 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, May.
    13. Zhang, Lan & Mykland, Per A. & Aït-Sahalia, Yacine, 2011. "Edgeworth expansions for realized volatility and related estimators," Journal of Econometrics, Elsevier, vol. 160(1), pages 190-203, January.
    14. 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.
    15. Neil Shephard, 2005. "Stochastic Volatility," Economics Papers 2005-W17, Economics Group, Nuffield College, University of Oxford.
    16. French, Kenneth R. & Roll, Richard, 1986. "Stock return variances : The arrival of information and the reaction of traders," Journal of Financial Economics, Elsevier, vol. 17(1), pages 5-26, September.
    17. 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," Economics Papers 2004-W28, Economics Group, Nuffield College, University of Oxford.
    18. Michael J. Barclay & Terrence Hendershott & D. Timothy McCormick, 2003. "Competition among Trading Venues: Information and Trading on Electronic Communications Networks," Journal of Finance, American Finance Association, vol. 58(6), pages 2637-2665, December.
    19. Jim Griffin & Roel Oomen, 2008. "Sampling Returns for Realized Variance Calculations: Tick Time or Transaction Time?," Econometric Reviews, Taylor & Francis Journals, vol. 27(1-3), pages 230-253.
    20. 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.
    21. 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.
    22. Neil Shephard, 2004. "Regular and Modified Kernel-Based Estimators of Integrated Variance: The Case with Independent Noise," Economics Series Working Papers 2004-FE-20, University of Oxford, Department of Economics.
    23. Michael J. Barclay & Terrence Hendershott & D. Timothy McCormick, 2003. "Competition among Trading Venues: Information and Trading on Electronic Communications Networks," Journal of Finance, American Finance Association, vol. 58(6), pages 2637-2666, December.
    24. 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.
    25. Oomen, Roel C.A., 2006. "Properties of Realized Variance Under Alternative Sampling Schemes," Journal of Business & Economic Statistics, American Statistical Association, vol. 24, pages 219-237, April.
    26. Yingying Li & Per A. Mykland, 2007. "Are volatility estimators robust with respect to modeling assumptions?," Papers 0709.0440, arXiv.org.
    27. Hans R. Stoll, 2000. "Presidential Address: Friction," Journal of Finance, American Finance Association, vol. 55(4), pages 1479-1514, August.
    28. Black, Fischer, 1986. "Noise," Journal of Finance, American Finance Association, vol. 41(3), pages 529-543, July.
    29. Harris, Lawrence, 1990. "Statistical Properties of the Roll Serial Covariance Bid/Ask Spread Estimator," Journal of Finance, American Finance Association, vol. 45(2), pages 579-590, June.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Yacine Ait-Sahalia & Jialin Yu, 2008. "High Frequency Market Microstructure Noise Estimates and Liquidity Measures," NBER Working Papers 13825, National Bureau of Economic Research, Inc.
    2. Zhang, Lan & Mykland, Per A. & Aït-Sahalia, Yacine, 2011. "Edgeworth expansions for realized volatility and related estimators," Journal of Econometrics, Elsevier, vol. 160(1), pages 190-203, January.
    3. Christensen, Kim & Kinnebrock, Silja & Podolskij, Mark, 2010. "Pre-averaging estimators of the ex-post covariance matrix in noisy diffusion models with non-synchronous data," Journal of Econometrics, Elsevier, vol. 159(1), pages 116-133, November.
    4. Barndorff-Nielsen, Ole E. & Hansen, Peter Reinhard & Lunde, Asger & Shephard, Neil, 2011. "Subsampling realised kernels," Journal of Econometrics, Elsevier, vol. 160(1), pages 204-219, January.
    5. Chaboud, Alain P. & Chiquoine, Benjamin & Hjalmarsson, Erik & Loretan, Mico, 2010. "Frequency of observation and the estimation of integrated volatility in deep and liquid financial markets," Journal of Empirical Finance, Elsevier, vol. 17(2), pages 212-240, March.
    6. Christensen, Kim & Oomen, Roel & Podolskij, Mark, 2010. "Realised quantile-based estimation of the integrated variance," Journal of Econometrics, Elsevier, vol. 159(1), pages 74-98, November.
    7. Xiu, Dacheng, 2010. "Quasi-maximum likelihood estimation of volatility with high frequency data," Journal of Econometrics, Elsevier, vol. 159(1), pages 235-250, November.
    8. Maheu, John M. & McCurdy, Thomas H., 2011. "Do high-frequency measures of volatility improve forecasts of return distributions?," Journal of Econometrics, Elsevier, vol. 160(1), pages 69-76, January.
    9. Nikolaus Hautsch & Mark Podolskij, 2013. "Preaveraging-Based Estimation of Quadratic Variation in the Presence of Noise and Jumps: Theory, Implementation, and Empirical Evidence," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 31(2), pages 165-183, April.
    10. Kalnina, Ilze, 2011. "Subsampling high frequency data," Journal of Econometrics, Elsevier, vol. 161(2), pages 262-283, April.
    11. Large, Jeremy, 2011. "Estimating quadratic variation when quoted prices change by a constant increment," Journal of Econometrics, Elsevier, vol. 160(1), pages 2-11, January.
    12. Neil Shephard & Dacheng Xiu, 2012. "Econometric analysis of multivariate realised QML: efficient positive semi-definite estimators of the covariation of equity prices," Economics Series Working Papers 604, University of Oxford, Department of Economics.
    13. Julien Chevallier & Benoît Sévi, 2011. "On the realized volatility of the ECX CO 2 emissions 2008 futures contract: distribution, dynamics and forecasting," Annals of Finance, Springer, vol. 7(1), pages 1-29, February.
    14. Ole E. Barndorff-Nielsen & Neil Shephard, 2005. "Variation, jumps, market frictions and high frequency data in financial econometrics," OFRC Working Papers Series 2005fe08, Oxford Financial Research Centre.
    15. Christensen, K. & Podolskij, M. & Thamrongrat, N. & Veliyev, B., 2017. "Inference from high-frequency data: A subsampling approach," Journal of Econometrics, Elsevier, vol. 197(2), pages 245-272.
    16. Hounyo, Ulrich & Gonçalves, Sílvia & Meddahi, Nour, 2017. "Bootstrapping Pre-Averaged Realized Volatility Under Market Microstructure Noise," Econometric Theory, Cambridge University Press, vol. 33(4), pages 791-838, August.
    17. 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.
    18. Bu, Ruijun & Hizmeri, Rodrigo & Izzeldin, Marwan & Murphy, Anthony & Tsionas, Mike, 2023. "The contribution of jump signs and activity to forecasting stock price volatility," Journal of Empirical Finance, Elsevier, vol. 70(C), pages 144-164.
    19. Jeremy Large, 2005. "Estimating Quadratic Variation When Quoted Prices Jump by a Constant Increment," Economics Series Working Papers 2005-FE-05, University of Oxford, Department of Economics.
    20. repec:dau:papers:123456789/4598 is not listed on IDEAS
    21. Shephard, Neil & Xiu, Dacheng, 2017. "Econometric analysis of multivariate realised QML: Estimation of the covariation of equity prices under asynchronous trading," Journal of Econometrics, Elsevier, vol. 201(1), pages 19-42.

    More about this item

    JEL classification:

    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:nbr:nberwo:11380. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: the person in charge (email available below). General contact details of provider: https://edirc.repec.org/data/nberrus.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.