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A Robust Estimation of Integrated Volatility under Round-off Errors, Micro-market Price Adjustments and Noises

Author

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  • Seisho Sato

    (Faculty of Economics, The University of Tokyo)

  • Naoto Kunitomo

    (Faculty of Economics, The University of Tokyo)

Abstract

For estimating the integrated volatility by using high frequency data, Kunitomo and Sato (2008, 2011, 2013) have proposed the Separating Information Maximum Likelihood (SIML) method when there are micro-market noises. The SIML estimator has reasonable nite sample properties and asymptotic properties when the sample size is large under reasonable conditions. We show that the SIML estimator has the robustness properties in the sense that it is consistent and has the stable convergence (i.e. the asymptotic normality in the deterministic case) when there are round- off errors and micro-market price adjustments and noises for the underlying (continuous time) stochastic process. The SIML estimation has also reasonable nite sample properties with these effects and dominate the existing methods such as the realized kernel method and the pre-averaging method in some situations. --

Suggested Citation

  • Seisho Sato & Naoto Kunitomo, 2015. "A Robust Estimation of Integrated Volatility under Round-off Errors, Micro-market Price Adjustments and Noises," CIRJE F-Series CIRJE-F-964, CIRJE, Faculty of Economics, University of Tokyo.
    • Handle: RePEc:tky:fseres:2015cf964
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    References listed on IDEAS

    as
    1. Kunitomo, Naoto & Sato, Seisho, 2013. "Separating Information Maximum Likelihood estimation of the integrated volatility and covariance with micro-market noise," The North American Journal of Economics and Finance, Elsevier, vol. 26(C), pages 282-309.
    2. Kunitomo, Naoto & Sato, Seisho, 2011. "The SIML estimation of realized volatility of the Nikkei-225 Futures and hedging coefficient with micro-market noise," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(7), pages 1272-1289.
    3. Zhang, Lan & Mykland, Per A. & Ait-Sahalia, Yacine, 2005. "A Tale of Two Time Scales: Determining Integrated Volatility With Noisy High-Frequency Data," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 1394-1411, December.
    4. Ole E. Barndorff-Nielsen & Peter Reinhard Hansen & Asger Lunde & Neil Shephard, 2008. "Designing Realized Kernels to Measure the ex post Variation of Equity Prices in the Presence of Noise," Econometrica, Econometric Society, vol. 76(6), pages 1481-1536, November.
    5. Naoto Kunitomo & Hiroumi Misaki & Seisho Sato, 2015. "The SIML Estimation of Integrated Covariance and Hedging Coefficient under Round-off Errors, Micro-market Price Adjustments and Random Sampling," CIRJE F-Series CIRJE-F-965, CIRJE, Faculty of Economics, University of Tokyo.
    6. Yacine Aït-Sahalia, 2005. "How Often to Sample a Continuous-Time Process in the Presence of Market Microstructure Noise," The Review of Financial Studies, Society for Financial Studies, vol. 18(2), pages 351-416.
    7. Markus Bibinger & Markus Reiß, 2014. "Spectral Estimation of Covolatility from Noisy Observations Using Local Weights," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 41(1), pages 23-50, March.
    8. Naoto Kunitomo & Seisho Sato, 2008. "Separating Information Maximum Likelihood Estimation of Realized Volatility and Covariance with Micro-Market Noise," CIRJE F-Series CIRJE-F-581, CIRJE, Faculty of Economics, University of Tokyo.
    9. Yacine Aït-Sahalia & Jean Jacod, 2014. "High-Frequency Financial Econometrics," Economics Books, Princeton University Press, edition 1, number 10261.
    10. Naoto Kunitomo & Seisho Sato, 1999. "Stationary and Non-stationary Simultaneous Switching Autoregressive Models with an Application to Financial Time Series," The Japanese Economic Review, Japanese Economic Association, vol. 50(2), pages 161-190, June.
    11. Amihud, Yakov & Mendelson, Haim, 1987. "Trading Mechanisms and Stock Returns: An Empirical Investigation," Journal of Finance, American Finance Association, vol. 42(3), pages 533-553, July.
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