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Generalized Flat-Top Realized Kernel Estimation of Ex-Post Variation of Asset Prices Contaminated by Noise

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  • Rasmus Tangsgaard Varneskov

    ()
    (Aarhus University and CREATES)

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    Abstract

    This paper introduces a new class of generalized at-top realized kernels for estimation of quadratic variation in the presence of market microstructure noise that is allowed to exhibit a non-trivial dependence structure and to be correlated with the ecient price process. The estimators in this class are shown to be consistent, asymptotically unbiased, and mixed gaussian with an optimal n^(1/4)-convergence rate. In addition, an ecient and asymptotically normal estimator of the long run variance of the market microstructure noise is provided along with novel and consistent estimators of the asymptotic variance of the at-top realized kernels and of the integrated quarticity, respectively, creating a powerful, unied framework for analyzing quadratic variation. A nite sample correction ensures non-negativity of the at-top realized kernels without a ecting asymptotic properties. Lastly, in an extensive simulation study, important practical issues such as the choice of kernel function and tuning parameters are addressed, the adequacy of the asymptotic distribution in nite samples is assessed, and it is shown that estimators in this class exhibit a superior bias and root mean squared error tradeo relative to competing estimators. The impact of using various realized estimators is illustrated in a small empirical application to noisy high frequency stock market data.

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    File URL: ftp://ftp.econ.au.dk/creates/rp/11/rp11_31.pdf
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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 2011-31.

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    Length: 61
    Date of creation: 01 Sep 2011
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    Handle: RePEc:aah:create:2011-31

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

    Related research

    Keywords: Bias Reduction; Nonparametric Estimation; Market Microstructure Noise; Quadratic Variation.;

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    1. Ole E. Barndorff-Nielsen & Peter Reinhard Hansen & Asger Lunde & Neil Shephard, 2008. "Multivariate realised kernels: consistent positive semi-definite estimators of the covariation of equity prices with noise and non-synchronous trading," OFRC Working Papers Series, Oxford Financial Research Centre 2008fe29, Oxford Financial Research Centre.
    2. Politis, D. N. & Romano, Joseph P. & Wolf, Michael, 1997. "Subsampling for heteroskedastic time series," Journal of Econometrics, Elsevier, Elsevier, vol. 81(2), pages 281-317, December.
    3. Andrews, Donald W. K., 1987. "Laws of Large Numbers for Dependent Non-Identically Distributed Random Variables," Working Papers, California Institute of Technology, Division of the Humanities and Social Sciences 645, California Institute of Technology, Division of the Humanities and Social Sciences.
    4. Ait-Sahalia, Yacine & Mykland, Per A. & Zhang, Lan, 2005. "Ultra high frequency volatility estimation with dependent microstructure noise," Discussion Paper Series 1: Economic Studies, Deutsche Bundesbank, Research Centre 2005,30, Deutsche Bundesbank, Research Centre.
    5. Kim Christensen & Silja Kinnebrock & Mark Podolskij, 2009. "Pre-averaging estimators of the ex-post covariance matrix in noisy diffusion models with non-synchronous data," CREATES Research Papers, School of Economics and Management, University of Aarhus 2009-45, School of Economics and Management, University of Aarhus.
    6. Ole E. Barndorff-Nielsen & Peter R. Hansen & Asger Lunde & Neil Shephard, 2006. "Subsampling realised kernels," OFRC Working Papers Series, Oxford Financial Research Centre 2006fe06, Oxford Financial Research Centre.
    7. Kalnina, Ilze, 2011. "Subsampling high frequency data," Journal of Econometrics, Elsevier, Elsevier, vol. 161(2), pages 262-283, April.
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    10. Torben G. Andersen & Dobrislav Dobrev & Ernst Schaumburg, 2011. "A Functional Filtering and Neighborhood Truncation Approach to Integrated Quarticity Estimation," NBER Working Papers 17152, National Bureau of Economic Research, Inc.
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    12. Donald W.K. Andrews, 2000. "Equivalence of the Higher-order Asymptotic Efficiency of k-step and Extremum Statistics," Cowles Foundation Discussion Papers, Cowles Foundation for Research in Economics, Yale University 1269, Cowles Foundation for Research in Economics, Yale University.
    13. Kim Christensen & Roel Oomen & Mark Podolskij, 2011. "Fact or friction: Jumps at ultra high frequency," CREATES Research Papers, School of Economics and Management, University of Aarhus 2011-19, School of Economics and Management, University of Aarhus.
    14. Meddahi, Nour & Mykland, Per & Shephard, Neil, 2011. "Realized Volatility," Journal of Econometrics, Elsevier, Elsevier, vol. 160(1), pages 1-1, January.
    15. F. M. Bandi & J. R. Russell, 2008. "Microstructure Noise, Realized Variance, and Optimal Sampling," Review of Economic Studies, Oxford University Press, vol. 75(2), pages 339-369.
    16. Maria Elvira Mancino & Paul Malliavin, 2002. "Fourier series method for measurement of multivariate volatilities," Finance and Stochastics, Springer, Springer, vol. 6(1), pages 49-61.
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    18. Politis, Dimitris N., 2011. "Higher-Order Accurate, Positive Semidefinite Estimation Of Large-Sample Covariance And Spectral Density Matrices," Econometric Theory, Cambridge University Press, Cambridge University Press, vol. 27(04), pages 703-744, August.
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