IDEAS home Printed from https://ideas.repec.org/
MyIDEAS: Login to save this paper or follow this series

Identifying the Brownian Covariation from the Co-Jumps Given Discrete Observations

  • Cecilia Mancini

    ()

    (Dipartimento di Matematica per le Decisioni, Universita' degli Studi di Firenze)

  • Fabio Gobbi

    ()

    (Department of Mathematical Economics, University of Bologna)

Registered author(s):

    In this paper we consider two semimartingales driven by Wiener processes and (possibly infinite activity) jumps. Given discrete observations we separately estimate the integrated covariation IC from the sum of the co-jumps. The Realized Covariation (RC) approaches the sum of IC with the co-jumps as the number of observations increases to infinity. Our threshold (or truncated) estimator \hat{IC}_n excludes from RC all the terms containing jumps in the finite activity case and the terms containing jumps over the threshold in the infinite activity case, and is consistent. To further measure the dependence between the two processes also the betas, \beta^{(1,2)} and \beta^{(2,1)}, and the correlation coefficient \rho^{(1,2)} among the Brownian semimartingale parts are consistently estimated. In presence of only finite activity jumps: 1) we reach CLTs for \hat{IC}_n, \hat\beta^{(i,j)} and \hat \rho^{(1,2)}; 2) combining thresholding with the observations selection proposed in Hayashi and Yoshida (2005) we reach an estimate of IC which is robust to asynchronous data. We report the results of an illustrative application, made in a web appendix (on www.dmd.unifi.it/upload/sub/persone/mancini/WebAppendix3.pdf), to two very different simulated realistic asset price models and we see that the finite sample performances of \hat{IC}_n and of the sum of the co-jumps estimator are good for values of the observation step large enough to avoid the typical problems arising in presence of microstructure noises in the data. However we find that the co-jumps estimators are more sensible than \hat{IC}_n to the choice of the threshold. Finding criteria for optimal threshold selection is object of further research.

    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: http://www.disei.unifi.it/upload/sub/pubblicazioni/repec/flo/workingpapers/storicodimad/2010n/dimadwp2010-05.pdf
    Download Restriction: no

    Paper provided by Universita' degli Studi di Firenze, Dipartimento di Scienze per l'Economia e l'Impresa in its series Working Papers - Mathematical Economics with number 2010-05.

    as
    in new window

    Length: 50 pages
    Date of creation: Mar 2010
    Date of revision:
    Handle: RePEc:flo:wpaper:2010-05
    Contact details of provider: Postal: Via delle Pandette 9 50127 - Firenze - Italy
    Phone: +39 055 2759707
    Fax: +39 055 2759913
    Web page: http://www.disei.unifi.it/
    Email:


    More information through EDIRC

    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. Takaki Hayashi & Shigeo Kusuoka, 2008. "Consistent estimation of covariation under nonsynchronicity," Statistical Inference for Stochastic Processes, Springer, vol. 11(1), pages 93-106, February.
    2. Barndorff-Nielsen, Ole Eiler & Graversen, Svend Erik & Jacod, Jean & Podolskij, Mark, 2004. "A central limit theorem for realised power and bipower variations of continuous semimartingales," Technical Reports 2004,51, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    3. Tim Bollerslev & Tzuo Hann Law & George Tauchen, 2007. "Risk, Jumps, and Diversification," CREATES Research Papers 2007-19, School of Economics and Management, University of Aarhus.
    4. Peter Carr & Helyette Geman, 2002. "The Fine Structure of Asset Returns: An Empirical Investigation," The Journal of Business, University of Chicago Press, vol. 75(2), pages 305-332, April.
    5. Cecilia Mancini, 2009. "Non-parametric Threshold Estimation for Models with Stochastic Diffusion Coefficient and Jumps," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 36(2), pages 270-296.
    6. Ole E. Barndorff-Nielsen & Neil Shephard, 2004. "Econometric Analysis of Realized Covariation: High Frequency Based Covariance, Regression, and Correlation in Financial Economics," Econometrica, Econometric Society, vol. 72(3), pages 885-925, 05.
    7. Egloff, Daniel & Leippold, Markus & Vanini, Paolo, 2007. "A simple model of credit contagion," Journal of Banking & Finance, Elsevier, vol. 31(8), pages 2475-2492, August.
    8. Neil Shephard, 2004. "A Central Limit Theorem for Realised Power and Bipower Variations of Continuous Semimartingales," Economics Series Working Papers 2004-FE-21, University of Oxford, Department of Economics.
    9. Jacod, Jean, 2008. "Asymptotic properties of realized power variations and related functionals of semimartingales," Stochastic Processes and their Applications, Elsevier, vol. 118(4), pages 517-559, April.
    10. Xin Huang & George Tauchen, 2005. "The Relative Contribution of Jumps to Total Price Variance," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 3(4), pages 456-499.
    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:flo:wpaper:2010-05. 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: (Michele Gori)

    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.