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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

We call the realized variance (RV), calculated with observed prices contaminated by (market) microstructure noises (MNs), the noise-contaminated RV (NCRV), and refer 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. 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. 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.

Suggested Citation

  • Daisuke Nagakura & Toshiaki Watanabe, 2011. "A State Space Approach to Estimating the Integrated Variance under the Existence of Market Microstructure Noise," Global COE Hi-Stat Discussion Paper Series gd11-200, Institute of Economic Research, Hitotsubashi University.
    • Handle: RePEc:hst:ghsdps:gd11-200
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    References listed on IDEAS

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    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.
    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.

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    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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