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

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  • 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.

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Bibliographic Info

Paper provided by Institute for Monetary and Economic Studies, Bank of Japan in its series IMES Discussion Paper Series with number 09-E-11.

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Date of creation: Mar 2009
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Handle: RePEc:ime:imedps:09-e-11

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Keywords: Realized Variance; Integrated Variance; Microstructure Noise;

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  1. 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.
  2. Meddahi, N., 2001. "An Eigenfunction Approach for Volatility Modeling," Cahiers de recherche, Centre interuniversitaire de recherche en économie quantitative, CIREQ 2001-29, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  3. Nelson, Daniel B., 1990. "ARCH models as diffusion approximations," Journal of Econometrics, Elsevier, Elsevier, vol. 45(1-2), pages 7-38.
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