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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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    File URL: http://www.cirje.e.u-tokyo.ac.jp/research/dp/2008/2008cf581.pdf
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    References listed on IDEAS

    as
    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," 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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    Cited by:

    1. 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.
    2. 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.
    3. Masato Ubukata & Toshiaki Watanabe, 2014. "Market variance risk premiums in Japan for asset predictability," Empirical Economics, Springer, vol. 47(1), pages 169-198, August.
    4. 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.
    5. 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.

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