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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
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    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, 2001. "An Eigenfunction Approach for Volatility Modeling," Cahiers de recherche 2001-29, Universite de Montreal, Departement de sciences economiques.
    4. Durbin, James & Koopman, Siem Jan, 2012. "Time Series Analysis by State Space Methods," OUP Catalogue, Oxford University Press, edition 2, number 9780199641178, Decembrie.
    5. Meddahi, Nour & Renault, Eric, 2004. "Temporal aggregation of volatility models," Journal of Econometrics, Elsevier, vol. 119(2), pages 355-379, April.
    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.
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    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.

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    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

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