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Limit Theorems for the Pre-averaged Hayashi-Yoshida Estimator with Random Sampling

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  • Yuta Koike
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    Abstract

    We will focus on estimating the integrated covariance of two diffusion processes observed in a nonsynchronous manner. The observation data is contaminated by some noise, which is possibly correlated with the returns of the diffusion processes, while the sampling times also possibly depend on the observed processes. This situation is much more realistic than those in which both of the noise and the sampling times are independent of the diffusion processes. In a high-frequency setting, we consider a modified version of the pre-averaged Hayashi- Yoshida estimator, and we show that such a kind of estimators has the consistency and the asymptotic mixed normality, and attains the optimal rate of convergence.

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    File URL: http://gcoe.ier.hit-u.ac.jp/research/discussion/2008/pdf/gd12-276.pdf
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    Bibliographic Info

    Paper provided by Institute of Economic Research, Hitotsubashi University in its series Global COE Hi-Stat Discussion Paper Series with number gd12-276.

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    Date of creation: Jan 2013
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    Handle: RePEc:hst:ghsdps:gd12-276

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    Related research

    Keywords: Endogenous noise; Hayashi-Yoshida estimator; Integrated covariance; Market microstructure noise; Nonsynchronous observations; Pre-averaging; Stable convergence; Strong predictability;

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    1. Kim Christensen & Silja Kinnebrock & Mark Podolskij, 2010. "Pre-averaging estimators of the ex-post covariance matrix in noisy diffusion models with non-synchronous data," Post-Print hal-00732537, HAL.
    2. Ingmar Nolte & Valeri Voev, 2009. "Least Squares Inference on Integrated Volatility and the Relationship between Efficient Prices and Noise," CREATES Research Papers 2009-16, School of Economics and Management, University of Aarhus.
    3. Corsi, Fulvio & Peluso, Stefano & Audrino, Francesco, 2012. "Missing in Asynchronicity: A Kalman-EM Approach for Multivariate Realized Covariance Estimation," Economics Working Paper Series 1202, University of St. Gallen, School of Economics and Political Science.
    4. Kalnina, Ilze & Linton, Oliver, 2008. "Estimating quadratic variation consistently in the presence of endogenous and diurnal measurement error," Journal of Econometrics, Elsevier, vol. 147(1), pages 47-59, November.
    5. Kim Christensen & Mark Podolskij & Mathias Vetter, 2011. "On covariation estimation for multivariate continuous Itô semimartingales with noise in non-synchronous observation schemes," CREATES Research Papers 2011-53, School of Economics and Management, University of Aarhus.
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