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Separating Information Maximum Likelihood estimation of the integrated volatility and covariance with micro-market noise

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  • Kunitomo, Naoto
  • Sato, Seisho

Abstract

For estimating the integrated volatility and covariance by using high frequency financial data, we propose the Separating Information Maximum Likelihood (SIML) method when there are possibly micro-market noises. The resulting estimator, which is represented as a specific quadratic form of returns, is simple and their properties have been investigated by Kunitomo and Sato (2008a, 2008b, 2010, 2011). We show that the SIML estimator has reasonable asymptotic properties; it is consistent and it has the asymptotic normality when the sample size is large and the integrated volatility is deterministic under general conditions including some non-Gaussian and volatility models. Based on simulations, we find that the SIML estimator has reasonable finite sample properties and 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 illustrate the use of SIML by analyzing Nikkei-225 futures, which are the derivatives of the major stock index in Japan.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:ecofin:v:26:y:2013:i:c:p:282-309
    DOI: 10.1016/j.najef.2013.02.006
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    References listed on IDEAS

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    1. 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.
    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.
    3. Yoshida, Yushi, 2013. "Intra-industry trade, fragmentation and export margins: An empirical examination of sub-regional international trade," The North American Journal of Economics and Finance, Elsevier, vol. 24(C), pages 125-138.
    4. 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.
    5. 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.
    6. 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.
    7. Peter Hansen & Jeremy Large & Asger Lunde, 2008. "Moving Average-Based Estimators of Integrated Variance," Econometric Reviews, Taylor & Francis Journals, vol. 27(1-3), pages 79-111.
    8. 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.
    9. 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.
    10. 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.
    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. 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.
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    Cited by:

    1. 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.
    2. 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.
    3. Naoto Kunitomo & Daisuke Kurisu, 2017. "Effects of Jumps and Small Noise in High-Frequency Financial Econometrics," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 24(1), pages 39-73, March.
    4. Li, Y-N. & Chen, J. & Linton, O., 2021. "Estimation of Common Factors for Microstructure Noise and Efficient Price in a High-frequency Dual Factor Model," Cambridge Working Papers in Economics 2150, Faculty of Economics, University of Cambridge.
    5. Shephard, Neil & Xiu, Dacheng, 2017. "Econometric analysis of multivariate realised QML: Estimation of the covariation of equity prices under asynchronous trading," Journal of Econometrics, Elsevier, vol. 201(1), pages 19-42.
    6. Chia-Lin Chang & Allen, David & McAleer, Michael, 2013. "Recent developments in financial economics and econometrics: An overview," The North American Journal of Economics and Finance, Elsevier, vol. 26(C), pages 217-226.
    7. Yuta Koike, 2017. "Time endogeneity and an optimal weight function in pre-averaging covariance estimation," Statistical Inference for Stochastic Processes, Springer, vol. 20(1), pages 15-56, April.
    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. Kurose, Yuta & Omori, Yasuhiro, 2020. "Multiple-block dynamic equicorrelations with realized measures, leverage and endogeneity," Econometrics and Statistics, Elsevier, vol. 13(C), pages 46-68.
    10. Yuta Kurose & Yasuhiro Omori, "undated". "Multiple-lock Dynamic Equicorrelations with Realized Measures, Leverage and Endogeneity," CIRJE F-Series CIRJE-F-1075, CIRJE, Faculty of Economics, University of Tokyo.
    11. Tatsuru Kikuchi & Toranosuke Onishi & Kenichi Ueda, 2021. "Price Stability of Cryptocurrencies as a Medium of Exchange," CARF F-Series CARF-F-526, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    12. 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.
    13. Yuta Kurose & Yasuhiro Omori, 2016. "Multiple-block Dynamic Equicorrelations with Realized Measures, Leverage and Endogeneity," CIRJE F-Series CIRJE-F-1024, CIRJE, Faculty of Economics, University of Tokyo.

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    More about this item

    Keywords

    Integrated volatility; Integrated covariance; Micro-market noise; High-frequency data; Separating Information Maximum Likelihood (SIML); Nikkei-225 futures;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C30 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - General

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