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

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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 have introduced the Separating Information Maximum Likelihood (SIML) method when there are possibly micro-market noises by Kunitomo and Sato (2008a, 2008b, 2010a, 2010b). The resulting estimator is simple and it has the representation as a specific quadratic form of returns. We show that 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 some non-Gaussian processes and some volatility models. Based on simulations, we find that the SIML estimator has reasonable finite sample properties and thus it would be useful for practice. The SIML estimator has the asymptotic robustness properties in the sense it is consistent when the noise terms are weakly dependent and they are endogenously correlated with the efficient market price process. We also apply our method to an analysis of Nikkei-225 Futures, which has been the major stock index in the Japanese financial sector.

Suggested Citation

  • 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.
    • Handle: RePEc:tky:fseres:2010cf758
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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. Christensen, Kim & Kinnebrock, Silja & Podolskij, Mark, 2010. "Pre-averaging estimators of the ex-post covariance matrix in noisy diffusion models with non-synchronous data," Journal of Econometrics, Elsevier, vol. 159(1), pages 116-133, November.
    4. 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.
    5. 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.
    6. Masato Ubukata & Kosuke Oya, 2009. "Estimation and Testing for Dependence in Market Microstructure Noise," Journal of Financial Econometrics, Oxford University Press, vol. 7(2), pages 106-151, Spring.
    7. 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.
    8. 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.
    9. Hansen, Peter R. & Lunde, Asger, 2006. "Realized Variance and Market Microstructure Noise," Journal of Business & Economic Statistics, American Statistical Association, vol. 24, pages 127-161, April.
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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. 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.

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