IDEAS home Printed from https://ideas.repec.org/a/taf/jnlbes/v30y2011i1p94-108.html
   My bibliography  Save this article

Least Squares Inference on Integrated Volatility and the Relationship Between Efficient Prices and Noise

Author

Listed:
  • Ingmar Nolte
  • Valeri Voev

Abstract

The expected value of sums of squared intraday returns (realized variance) gives rise to a least squares regression which adapts itself to the assumptions of the noise process and allows for joint inference on integrated variance ( ), noise moments, and price-noise relations. In the iid noise case, we derive the asymptotic variance of the and noise variance estimators and show that they are consistent. The joint estimation approach is particularly attractive as it reveals important characteristics of the noise process which can be related to liquidity and market efficiency. The analysis of dependence between the price and noise processes provides an often missing link to market microstructure theory. We find substantial differences in the noise characteristics of trade and quote data arising from the effect of distinct market microstructure frictions. This article has supplementary material online.

Suggested Citation

  • Ingmar Nolte & Valeri Voev, 2011. "Least Squares Inference on Integrated Volatility and the Relationship Between Efficient Prices and Noise," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 30(1), pages 94-108, April.
    • Handle: RePEc:taf:jnlbes:v:30:y:2011:i:1:p:94-108
    DOI: 10.1080/10473289.2011.637876
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1080/10473289.2011.637876
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1080/10473289.2011.637876?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. 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.
    2. Hausman, Jerry, 2015. "Specification tests in econometrics," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 38(2), pages 112-134.
    3. 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.
    4. 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.
    5. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Paul Labys, 2003. "Modeling and Forecasting Realized Volatility," Econometrica, Econometric Society, vol. 71(2), pages 579-625, March.
    6. repec:oxf:wpaper:264 is not listed on IDEAS
    7. Bandi, Federico M. & Russell, Jeffrey R., 2006. "Separating microstructure noise from volatility," Journal of Financial Economics, Elsevier, vol. 79(3), pages 655-692, March.
    8. O. E. Barndorff-Nielsen & P. Reinhard Hansen & A. Lunde & N. Shephard, 2009. "Realized kernels in practice: trades and quotes," Econometrics Journal, Royal Economic Society, vol. 12(3), pages 1-32, November.
    9. Lo, Andrew W. & Craig MacKinlay, A., 1990. "An econometric analysis of nonsynchronous trading," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 181-211.
    10. 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.
    11. Roel C. A. Oomen, 2005. "Properties of Bias-Corrected Realized Variance Under Alternative Sampling Schemes," Journal of Financial Econometrics, Oxford University Press, vol. 3(4), pages 555-577.
    12. Gençay, Ramazan & Dacorogna, Michel & Muller, Ulrich A. & Pictet, Olivier & Olsen, Richard, 2001. "An Introduction to High-Frequency Finance," Elsevier Monographs, Elsevier, edition 1, number 9780122796715.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Yuta Koike, 2013. "Limit Theorems for the Pre-averaged Hayashi-Yoshida Estimator with Random Sampling," Global COE Hi-Stat Discussion Paper Series gd12-276, Institute of Economic Research, Hitotsubashi University.
    2. Roxana Halbleib & Valerie Voev, 2011. "Forecasting Covariance Matrices: A Mixed Frequency Approach," Working Papers ECARES ECARES 2011-002, ULB -- Universite Libre de Bruxelles.
    3. Varneskov, Rasmus & Voev, Valeri, 2013. "The role of realized ex-post covariance measures and dynamic model choice on the quality of covariance forecasts," Journal of Empirical Finance, Elsevier, vol. 20(C), pages 83-95.
    4. Selma Chaker, 2013. "Volatility and Liquidity Costs," Staff Working Papers 13-29, Bank of Canada.
    5. Roxana Halbleib & Valeri Voev, 2016. "Forecasting Covariance Matrices: A Mixed Approach," Journal of Financial Econometrics, Oxford University Press, vol. 14(2), pages 383-417.
    6. Vladim'ir Hol'y & Petra Tomanov'a, 2020. "Streaming Approach to Quadratic Covariation Estimation Using Financial Ultra-High-Frequency Data," Papers 2003.13062, arXiv.org, revised Dec 2021.

    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. 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.
    2. 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.
    3. Fleming, Jeff & Paye, Bradley S., 2011. "High-frequency returns, jumps and the mixture of normals hypothesis," Journal of Econometrics, Elsevier, vol. 160(1), pages 119-128, January.
    4. Griffin, Jim E. & Oomen, Roel C.A., 2011. "Covariance measurement in the presence of non-synchronous trading and market microstructure noise," Journal of Econometrics, Elsevier, vol. 160(1), pages 58-68, January.
    5. 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.
    6. Chun Liu & John M. Maheu, 2009. "Forecasting realized volatility: a Bayesian model-averaging approach," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 24(5), pages 709-733.
    7. Bollerslev, Tim & Patton, Andrew J. & Quaedvlieg, Rogier, 2016. "Exploiting the errors: A simple approach for improved volatility forecasting," Journal of Econometrics, Elsevier, vol. 192(1), pages 1-18.
    8. Torben G. Andersen & Viktor Todorov, 2009. "Realized Volatility and Multipower Variation," CREATES Research Papers 2009-49, Department of Economics and Business Economics, Aarhus University.
    9. 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.
    10. Chun Liu & John M. Maheu, 2008. "Are There Structural Breaks in Realized Volatility?," Journal of Financial Econometrics, Oxford University Press, vol. 6(3), pages 326-360, Summer.
    11. Neil Shephard & Kevin Sheppard, 2010. "Realising the future: forecasting with high-frequency-based volatility (HEAVY) models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 25(2), pages 197-231.
    12. Sílvia Gonçalves & Ulrich Hounyo & Nour Meddahi, 2014. "Bootstrap Inference for Pre-averaged Realized Volatility based on Nonoverlapping Returns," Journal of Financial Econometrics, Oxford University Press, vol. 12(4), pages 679-707.
    13. Michael McAleer & Marcelo Medeiros, 2008. "Realized Volatility: A Review," Econometric Reviews, Taylor & Francis Journals, vol. 27(1-3), pages 10-45.
    14. 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.
    15. Nicholas Taylor, 2008. "The predictive value of temporally disaggregated volatility: evidence from index futures markets," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 27(8), pages 721-742.
    16. Bandi, Federico M. & Russell, Jeffrey R., 2011. "Market microstructure noise, integrated variance estimators, and the accuracy of asymptotic approximations," Journal of Econometrics, Elsevier, vol. 160(1), pages 145-159, January.
    17. Bannouh, K. & van Dijk, D.J.C. & Martens, M.P.E., 2008. "Range-based covariance estimation using high-frequency data: The realized co-range," Econometric Institute Research Papers EI 2007-53, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    18. Bandi, Federico M. & Russell, Jeffrey R. & Yang, Chen, 2008. "Realized volatility forecasting and option pricing," Journal of Econometrics, Elsevier, vol. 147(1), pages 34-46, November.
    19. 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.
    20. Peter Reinhard Hansen & Zhuo Huang, 2016. "Exponential GARCH Modeling With Realized Measures of Volatility," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 34(2), pages 269-287, April.

    More about this item

    JEL classification:

    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)
    • F31 - International Economics - - International Finance - - - Foreign Exchange
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models

    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:taf:jnlbes:v:30:y:2011:i:1:p:94-108. 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: Chris Longhurst (email available below). General contact details of provider: http://www.tandfonline.com/UBES20 .

    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.