IDEAS home Printed from https://ideas.repec.org/p/ime/imedps/09-e-11.html
   My bibliography  Save this paper

A State Space Approach to Estimating the Integrated Variance and Microstructure Noise Component

Author

Listed:
  • Daisuke Nagakura

    (Institute for Monetary and Economic Studies, Bank of Japan (E-mail: daisuke.nagakura@boj.or.jp))

  • Toshiaki Watanabe

    (Professor, Institute of Economic Research, Hitotsubashi University, and Institute for Monetary and Economic Studies, Bank of Japan (E-mail: watanabe@hit-u.ac.jp, toshiaki.watanabe@boj.or.jp))

Abstract

We call the realized variance (RV) calculated with observed prices contaminated by microstructure noises (MNs) the noise-contaminated RV (NCRV) and refer to the component in the NCRV associated with the MNs as the MN component. This paper develops a method for estimating the integrated variance (IV) and MN component simultaneously, extending the state space method proposed by Barndorff-Nielsen and Shephard (2002). Our extension is based on the result obtained in Meddahi (2003), namely, when the true log-price process follows a general class of continuous-time stochastic volatility (SV) models, the IV follows an ARMA process. We represent the NCRV by a state space form and show that the state space form parameters are not identifiable; however, they can be expressed as functions of fewer identifiable parameters. We illustrate how to estimate these parameters. The proposed method is applied to yen/dollar exchange rate data. We find that the magnitude of the MN component is, on average, about 21%-48 % of the NCRV, depending on the sampling frequency.

Suggested Citation

  • Daisuke Nagakura & Toshiaki Watanabe, 2009. "A State Space Approach to Estimating the Integrated Variance and Microstructure Noise Component," IMES Discussion Paper Series 09-E-11, Institute for Monetary and Economic Studies, Bank of Japan.
    • Handle: RePEc:ime:imedps:09-e-11
    as

    Download full text from publisher

    File URL: http://www.imes.boj.or.jp/research/papers/english/09-E-11.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Nour Meddahi, 2003. "ARMA representation of integrated and realized variances," Econometrics Journal, Royal Economic Society, vol. 6(2), pages 335-356, December.
    2. Nelson, Daniel B., 1990. "ARCH models as diffusion approximations," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 7-38.
    3. Meddahi, Nour & Renault, Eric, 2004. "Temporal aggregation of volatility models," Journal of Econometrics, Elsevier, vol. 119(2), pages 355-379, April.
    4. MEDDAHI, Nour, 2001. "An Eigenfunction Approach for Volatility Modeling," Cahiers de recherche 2001-29, Universite de Montreal, Departement de sciences economiques.
    5. Durbin, James & Koopman, Siem Jan, 2012. "Time Series Analysis by State Space Methods," OUP Catalogue, Oxford University Press, edition 2, number 9780199641178.
    6. Nour Meddahi, 2002. "ARMA Representation of Two-Factor Models," CIRANO Working Papers 2002s-92, CIRANO.
    7. 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.
    8. Shephard, Neil (ed.), 2005. "Stochastic Volatility: Selected Readings," OUP Catalogue, Oxford University Press, number 9780199257201.
    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. Daisuke Nagakura & Toshiaki Watanabe, 2015. "A State Space Approach to Estimating the Integrated Variance under the Existence of Market Microstructure Noise," Journal of Financial Econometrics, Oxford University Press, vol. 13(1), pages 45-82.

    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. Kim, Jihyun & Meddahi, Nour, 2020. "Volatility regressions with fat tails," Journal of Econometrics, Elsevier, vol. 218(2), pages 690-713.
    2. Daisuke Nagakura & Toshiaki Watanabe, 2015. "A State Space Approach to Estimating the Integrated Variance under the Existence of Market Microstructure Noise," Journal of Financial Econometrics, Oxford University Press, vol. 13(1), pages 45-82.
    3. Torben G. Andersen & Tim Bollerslev & Nour Meddahi, 2004. "Analytical Evaluation Of Volatility Forecasts," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 45(4), pages 1079-1110, November.
    4. Ding, Yashuang (Dexter), 2023. "A simple joint model for returns, volatility and volatility of volatility," Journal of Econometrics, Elsevier, vol. 232(2), pages 521-543.
    5. Nour Meddahi, 2002. "ARMA Representation of Two-Factor Models," CIRANO Working Papers 2002s-92, CIRANO.
    6. Nour Meddahi, 2003. "ARMA representation of integrated and realized variances," Econometrics Journal, Royal Economic Society, vol. 6(2), pages 335-356, December.
    7. Nour Meddahi, 2002. "A theoretical comparison between integrated and realized volatility," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 17(5), pages 479-508.
    8. Corradi, Valentina & Distaso, Walter & Swanson, Norman R., 2009. "Predictive density estimators for daily volatility based on the use of realized measures," Journal of Econometrics, Elsevier, vol. 150(2), pages 119-138, June.
    9. Neil Shephard & Torben Andersen, 2008. "Stochastic Volatility: Origins and Overview," Economics Papers 2008-W04, Economics Group, Nuffield College, University of Oxford.
    10. Valentina Corradi & Norman Swanson & Walter Distaso, 2006. "Predictive Inference for Integrated Volatility," Departmental Working Papers 200616, Rutgers University, Department of Economics.
    11. Siem Jan Koopman & Rutger Lit & André Lucas, 2017. "Intraday Stochastic Volatility in Discrete Price Changes: The Dynamic Skellam Model," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(520), pages 1490-1503, October.
    12. Jihyun Kim & Nour Meddahi, 2020. "Volatility Regressions with Fat Tails," Post-Print hal-03142647, HAL.
    13. Meddahi, Nour & Renault, Eric & Werker, Bas, 2006. "GARCH and irregularly spaced data," Economics Letters, Elsevier, vol. 90(2), pages 200-204, February.
    14. Barndorff-Nielsen, Ole E. & Shephard, Neil, 2006. "Impact of jumps on returns and realised variances: econometric analysis of time-deformed Levy processes," Journal of Econometrics, Elsevier, vol. 131(1-2), pages 217-252.
    15. 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.
    16. Andreou, Elena & Ghysels, Eric, 2006. "Monitoring disruptions in financial markets," Journal of Econometrics, Elsevier, vol. 135(1-2), pages 77-124.
    17. Barndorff-Nielsen, Ole E. & Shephard, Neil, 2006. "Impact of jumps on returns and realised variances: econometric analysis of time-deformed Levy processes," Journal of Econometrics, Elsevier, vol. 131(1-2), pages 217-252.

    More about this item

    Keywords

    Realized Variance; Integrated Variance; Microstructure Noise;
    All these keywords.

    JEL classification:

    • C0 - Mathematical and Quantitative Methods - - General
    • G0 - Financial Economics - - General

    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:ime:imedps:09-e-11. 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: Kinken (email available below). General contact details of provider: https://edirc.repec.org/data/imegvjp.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.