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A State Space Approach to Estimating the Integrated Variance under the Existence of Market Microstructure Noise

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  • Daisuke Nagakura
  • Toshiaki Watanabe

Abstract

Abstract We call the realized variance (RV) calculated with observed prices contaminated by (market) microstructure noises (MNs) the noise-contaminated RV (NCRV), referring to the bias component in the NCRV associated with the MNs as the MN component. This paper develops a state space method for estimating the integrated variance (IV) and MN component. 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 identifiable parameters. We illustrate how to estimate these parameters. The proposed method also serves as a convenient way for estimating a general class of continuous-time stochastic volatility (SV) models under the existence of MN. We apply the proposed method to yen/dollar exchange rate data, where we find that most of the variation in NCRV is of the MN component.

Suggested Citation

  • Daisuke Nagakura & Toshiaki Watanabe, 2010. "A State Space Approach to Estimating the Integrated Variance under the Existence of Market Microstructure Noise," Global COE Hi-Stat Discussion Paper Series gd09-115, Institute of Economic Research, Hitotsubashi University.
  • Handle: RePEc:hst:ghsdps:gd09-115
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    References listed on IDEAS

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    1. Andersen T. G & Bollerslev T. & Diebold F. X & Labys P., 2001. "The Distribution of Realized Exchange Rate Volatility," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 42-55, March.
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    9. 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, Society for Financial Econometrics, vol. 13(1), pages 45-82.
    10. 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.
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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, Society for Financial Econometrics, vol. 13(1), pages 45-82.
    2. Masato Ubukata & Toshiaki Watanabe, 2011. "Pricing Nikkei 225 Options Using Realized Volatility," IMES Discussion Paper Series 11-E-18, Institute for Monetary and Economic Studies, Bank of Japan.
    3. Masato Ubukata & Toshiaki Watanabe, 2013. "Pricing Nikkei 225 Options Using Realized Volatility," Global COE Hi-Stat Discussion Paper Series gd12-273, Institute of Economic Research, Hitotsubashi University.

    More about this item

    Keywords

    Realized Variance; Integrated Variance; Microstructure Noise; State Space; Identification; Exchange Rate;

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods

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