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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)

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.

Suggested Citation

  • Rasmus Tangsgaard Varneskov, 2011. "Flat-Top Realized Kernel Estimation of Quadratic Covariation with Non-Synchronous and Noisy Asset Prices," CREATES Research Papers 2011-35, Department of Economics and Business Economics, Aarhus University.
  • Handle: RePEc:aah:create:2011-35
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    File URL: ftp://ftp.econ.au.dk/creates/rp/11/rp11_35.pdf
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    References listed on IDEAS

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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, vol. 124(8), pages 2699-2753.

    More about this item

    Keywords

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

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

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