IDEAS home Printed from https://ideas.repec.org/
MyIDEAS: Log in (now much improved!) to save this paper

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

Listed author(s):
  • Rasmus Tangsgaard Varneskov

    ()

    (Aarhus University and CREATES)

Registered author(s):

    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.

    If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.

    File URL: ftp://ftp.econ.au.dk/creates/rp/11/rp11_35.pdf
    Download Restriction: no

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

    as
    in new window

    Length: 42
    Date of creation: 27 Sep 2011
    Handle: RePEc:aah:create:2011-35
    Contact details of provider: Web page: http://www.econ.au.dk/afn/

    References listed on IDEAS
    Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

    as
    in new window


    1. Abadir,Karim M. & Magnus,Jan R., 2005. "Matrix Algebra," Cambridge Books, Cambridge University Press, number 9780521537469, March.
    2. O. E. Barndorff-Nielsen & P. Reinhard Hansen & A. Lunde & N. Shephard, 2009. "Realized kernels in practice: trades and quotes," Econometrics Journal, Royal Economic Society, vol. 12(3), pages 1-32, November.
    3. Francis X. Diebold & Georg Strasser, 2013. "On the Correlation Structure of Microstructure Noise: A Financial Economic Approach," Review of Economic Studies, Oxford University Press, vol. 80(4), pages 1304-1337.
    4. 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.
    5. Roxana Chiriac & Valeri Voev, 2011. "Modelling and forecasting multivariate realized volatility," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 26(6), pages 922-947, September.
    6. Dahlhaus, Rainer, 2009. "Local inference for locally stationary time series based on the empirical spectral measure," Journal of Econometrics, Elsevier, vol. 151(2), pages 101-112, August.
    7. Jagannathan, Ravi & Wang, Zhenyu, 1996. " The Conditional CAPM and the Cross-Section of Expected Returns," Journal of Finance, American Finance Association, vol. 51(1), pages 3-53, March.
    8. Aït-Sahalia, Yacine & Mykland, Per A. & Zhang, Lan, 2011. "Ultra high frequency volatility estimation with dependent microstructure noise," Journal of Econometrics, Elsevier, vol. 160(1), pages 160-175, January.
    9. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Paul Labys, 2003. "Modeling and Forecasting Realized Volatility," Econometrica, Econometric Society, vol. 71(2), pages 579-625, March.
    10. Glosten, Lawrence R. & Milgrom, Paul R., 1985. "Bid, ask and transaction prices in a specialist market with heterogeneously informed traders," Journal of Financial Economics, Elsevier, vol. 14(1), pages 71-100, March.
    11. Mark Podolskij & Mathias Vetter, 2010. "Understanding limit theorems for semimartingales: a short survey," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 64(s1), pages 329-351.
    12. Kalnina, Ilze, 2011. "Subsampling high frequency data," Journal of Econometrics, Elsevier, vol. 161(2), pages 262-283, April.
    13. repec:cup:cbooks:9780521822893 is not listed on IDEAS
    14. 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.
    15. 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.
    16. Mancini, Cecilia & Gobbi, Fabio, 2012. "Identifying The Brownian Covariation From The Co-Jumps Given Discrete Observations," Econometric Theory, Cambridge University Press, vol. 28(02), pages 249-273, April.
    17. 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.
    18. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-858, May.
    19. Shin S. Ikeda, 2015. "Two-Scale Realized Kernels: A Univariate Case," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 13(1), pages 126-165.
    20. Masato Ubukata & Kosuke Oya, 2009. "Estimation and Testing for Dependence in Market Microstructure Noise," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 7(2), pages 106-151, Spring.
    21. Griffin, Jim E. & Oomen, Roel C.A., 2011. "Covariance measurement in the presence of non-synchronous trading and market microstructure noise," Journal of Econometrics, Elsevier, vol. 160(1), pages 58-68, January.
    22. Valeri Voev & Asger Lunde, 2007. "Integrated Covariance Estimation using High-frequency Data in the Presence of Noise," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 5(1), pages 68-104.
    23. Ferson, Wayne E & Harvey, Campbell R, 1991. "The Variation of Economic Risk Premiums," Journal of Political Economy, University of Chicago Press, vol. 99(2), pages 385-415, April.
    24. Varneskov, Rasmus & Voev, Valeri, 2013. "The role of realized ex-post covariance measures and dynamic model choice on the quality of covariance forecasts," Journal of Empirical Finance, Elsevier, vol. 20(C), pages 83-95.
    25. LAURENT, Sebastien & ROMBOUTS, Jeroen V.K. & VIOLANTE, FRANCESCO, 2009. "Consistent ranking of multivariate volatility models," CORE Discussion Papers 2009002, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    26. 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.
    Full references (including those not matched with items on IDEAS)

    This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

    When requesting a correction, please mention this item's handle: RePEc:aah:create:2011-35. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: ()

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If references are entirely missing, you can add them using this form.

    If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.