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Separating Information Maximum Likelihood Estimation of Realized Volatility and Covariance with Micro-Market Noise

Author

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  • Naoto Kunitomo

    (Faculty of Economics, University of Tokyo)

  • Seisho Sato

    (Institute of Statistical Mathematics)

Abstract

For estimating the realized volatility and covariance by using high frequency data, we introduce the Separating Information Maximum Likelihood (SIML) method when there are possibly micro-market noises. The resulting estimator is simple and it has the representation as a specific quadratic form of returns. The SIML estimator has reasonable asymptotic properties; it is consistent and it has the asymptotic normality (or the stable convergence in the general case) when the sample size is large under general conditions including non-Gaussian processes and volatility models. Based on simulations, we find that the SIML estimator has reasonable finite sample properties and thus it would be useful for practice. It is also possible to use the limiting distribution of the SIML estimator for constructing testing procedures and confidence intervals.

Suggested Citation

  • 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.
    • Handle: RePEc:tky:fseres:2008cf581
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. 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.
    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.
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    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. Masato Ubukata & Toshiaki Watanabe, 2014. "Market variance risk premiums in Japan for asset predictability," Empirical Economics, Springer, vol. 47(1), pages 169-198, August.
    3. Misaki, Hiroumi & Kunitomo, Naoto, 2015. "On robust properties of the SIML estimation of volatility under micro-market noise and random sampling," International Review of Economics & Finance, Elsevier, vol. 40(C), pages 265-281.
    4. Ubukata, Masato & Watanabe, Toshiaki, 2015. "Evaluating the performance of futures hedging using multivariate realized volatility," Journal of the Japanese and International Economies, Elsevier, vol. 38(C), pages 148-171.
    5. Masato Ubukata & Toshiaki Watanabe, 2014. "Pricing Nikkei 225 Options Using Realized Volatility," The Japanese Economic Review, Japanese Economic Association, vol. 65(4), pages 431-467, December.
    6. Masato Ubukata & Toshiaki Watanabe, 2011. "Market Variance Risk Premiums in Japan as Predictor Variables and Indicators of Risk Aversion," Global COE Hi-Stat Discussion Paper Series gd11-214, Institute of Economic Research, Hitotsubashi University.
    7. 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.
    8. Naoto Kunitomo & Seisho Sato, 2015. "Trend, Seasonality and Economic Time Series:the Nonstationary Errors-in-variables Models," CIRJE F-Series CIRJE-F-977, CIRJE, Faculty of Economics, University of Tokyo.
    9. Naoto Kunitomo & Hiroumi Misaki, 2013. "The SIML Estimation of Integrated Covariance and Hedging Coefficient under Micro-market noise and Random Sampling," CIRJE F-Series CIRJE-F-893, CIRJE, Faculty of Economics, University of Tokyo.
    10. 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," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 22(3), pages 333-368, September.
    11. Naoto Kunitomo & Seisho Sato, 2010. "Robustness of the Separating Information Maximum Likelihood Estimation of Realized Volatility with Micro-Market Noise," CIRJE F-Series CIRJE-F-733, CIRJE, Faculty of Economics, University of Tokyo.
    12. 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.
    13. Hiroumi Misaki & Naoto Kunitomo, 2013. "On Robust Properties of the SIML Estimation of Volatility under Micro-market noise and Random Sampling," CIRJE F-Series CIRJE-F-892, CIRJE, Faculty of Economics, University of Tokyo.
    14. 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.
    15. Naoto Kunitomo & Seisho Sato, 2010. "On Properties of Separating Information Maximum Likelihood Estimation of Realized Volatility and Covariance with Micro-Market Noise," CARF F-Series CARF-F-228, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    16. 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.
    17. Naoto Kunitomo & Seisho Sato, 2010. "On Properties of Separating Information Maximum Likelihood Estimation of Realized Volatility and Covariance with Micro-Market Noise," CIRJE F-Series CIRJE-F-758, CIRJE, Faculty of Economics, University of Tokyo.

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