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Flat-Top Realized Kernel Estimation of Quadratic Covariation with Non-Synchronous and Noisy Asset Prices

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  • Rasmus Tangsgaard Varneskov

    ()
    (Aarhus University and CREATES)

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    Abstract

    This paper extends the class of generalized at-top realized kernels, introduced in Varneskov (2011), to the multivariate case, where quadratic covariation of non-synchronously observed asset prices is estimated in the presence of market microstructure noise that is allowed to exhibit serial dependence and to be correlated with the efficient price process. Estimators in this class are shown to posses desirable statistical properties such as consistency, asymptotic normality, and asymptotic unbiasedness at an optimal n^(1/4)-convergence rate. A finite sample correction based on projections of symmetric matrices ensures positive (semi-)definiteness without altering asymptotic properties of the class of estimators. The finite sample correction admits non-linear transformations of the estimated covariance matrix such as correlations and realized betas, and it can be used in portfolio optimization problems. These transformations are all shown to inherit the desirable asymptotic properties of the generalized at-top realized kernels. A simulation study shows that the class of estimators has a superior finite sample tradeoff between bias and root mean squared error relative to competing estimators. Lastly, two small empirical applications to high frequency stock market data illustrate the bias reduction relative to competing estimators in estimating correlations, realized betas, and mean-variance frontiers, as well as the use of the new estimators in the dynamics of hedging.

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    Bibliographic Info

    Paper provided by School of Economics and Management, University of Aarhus in its series CREATES Research Papers with number 2011-35.

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    Length: 42
    Date of creation: 27 Sep 2011
    Date of revision:
    Handle: RePEc:aah:create:2011-35

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    Web page: http://www.econ.au.dk/afn/

    Related research

    Keywords: Bias Reduction; Nonparametric Estimation; Market Microstructure Noise; Portfolio Optimization; Quadratic Covariation; Realized Beta.;

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    Cited by:
    1. Koike, Yuta, 2014. "Limit theorems for the pre-averaged Hayashi–Yoshida estimator with random sampling," Stochastic Processes and their Applications, Elsevier, Elsevier, vol. 124(8), pages 2699-2753.

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