A State Space Approach to Estimating the Integrated Variance and Microstructure Noise Component
AbstractWe 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 InfoPaper provided by Institute for Monetary and Economic Studies, Bank of Japan in its series IMES Discussion Paper Series with number 09-E-11.
Date of creation: Mar 2009
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Realized Variance; Integrated Variance; Microstructure Noise;
Other versions of this item:
- Daisuke Nagakura & Toshiaki Watanabe, 2009. "A State Space Approach to Estimating the Integrated Variance and Microstructure Noise Component," Global COE Hi-Stat Discussion Paper Series gd09-055, Institute of Economic Research, Hitotsubashi University.
This paper has been announced in the following NEP Reports:
- NEP-ALL-2009-03-28 (All new papers)
- NEP-ECM-2009-03-28 (Econometrics)
- NEP-ETS-2009-03-28 (Econometric Time Series)
- NEP-MST-2009-03-28 (Market Microstructure)
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Nour Meddahi, 2001.
"An Eigenfunction Approach for Volatility Modeling,"
CIRANO Working Papers
- Meddahi, N., 2001. "An Eigenfunction Approach for Volatility Modeling," Cahiers de recherche 2001-29, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
- MEDDAHI, Nour, 2001. "An Eigenfunction Approach for Volatility Modeling," Cahiers de recherche 2001-29, Universite de Montreal, Departement de sciences economiques.
- 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.
- Nelson, Daniel B., 1990. "ARCH models as diffusion approximations," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 7-38.
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