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

Sparse Kalman Filtering Approaches to Covariance Estimation from High Frequency Data in the Presence of Jumps

Listed author(s):
  • Michael Ho
  • Jack Xin
Registered author(s):

    Estimation of the covariance matrix of asset returns from high frequency data is complicated by asynchronous returns, market mi- crostructure noise and jumps. One technique for addressing both asynchronous returns and market microstructure is the Kalman-EM (KEM) algorithm. However the KEM approach assumes log-normal prices and does not address jumps in the return process which can corrupt estimation of the covariance matrix. In this paper we extend the KEM algorithm to price models that include jumps. We propose two sparse Kalman filtering approaches to this problem. In the first approach we develop a Kalman Expectation Conditional Maximization (KECM) algorithm to determine the un- known covariance as well as detecting the jumps. For this algorithm we consider Laplace and the spike and slab jump models, both of which promote sparse estimates of the jumps. In the second method we take a Bayesian approach and use Gibbs sampling to sample from the posterior distribution of the covariance matrix under the spike and slab jump model. Numerical results using simulated data show that each of these approaches provide for improved covariance estima- tion relative to the KEM method in a variety of settings where jumps occur.

    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://arxiv.org/pdf/1602.02185
    File Function: Latest version
    Download Restriction: no

    Paper provided by arXiv.org in its series Papers with number 1602.02185.

    as
    in new window

    Length:
    Date of creation: Feb 2016
    Date of revision: Apr 2016
    Handle: RePEc:arx:papers:1602.02185
    Contact details of provider: Web page: http://arxiv.org/

    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. Lo, Andrew W. & Craig MacKinlay, A., 1990. "An econometric analysis of nonsynchronous trading," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 181-211.
    2. repec:hal:journl:peer-00815564 is not listed on IDEAS
    3. Zhang, Lan, 2011. "Estimating covariation: Epps effect, microstructure noise," Journal of Econometrics, Elsevier, vol. 160(1), pages 33-47, January.
    4. Chan, Wing H & Maheu, John M, 2002. "Conditional Jump Dynamics in Stock Market Returns," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(3), pages 377-389, July.
    5. Barndorff-Nielsen, Ole E. & Hansen, Peter Reinhard & Lunde, Asger & Shephard, Neil, 2011. "Multivariate realised kernels: Consistent positive semi-definite estimators of the covariation of equity prices with noise and non-synchronous trading," Journal of Econometrics, Elsevier, vol. 162(2), pages 149-169, June.
    6. Fulvio Corsi & Stefano Peluso & Francesco Audrino, 2015. "Missing in Asynchronicity: A Kalman‐em Approach for Multivariate Realized Covariance Estimation," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 30(3), pages 377-397, April.
    7. Jianqing Fan & Yingying Li & Ke Yu, 2012. "Vast Volatility Matrix Estimation Using High-Frequency Data for Portfolio Selection," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(497), pages 412-428, March.
    8. Roll, Richard, 1984. " A Simple Implicit Measure of the Effective Bid-Ask Spread in an Efficient Market," Journal of Finance, American Finance Association, vol. 39(4), pages 1127-1139, September.
    9. Victor DeMiguel & Lorenzo Garlappi & Raman Uppal, 2009. "Optimal Versus Naive Diversification: How Inefficient is the 1-N Portfolio Strategy?," Review of Financial Studies, Society for Financial Studies, vol. 22(5), pages 1915-1953, May.
    10. John M. Maheu & Thomas H. McCurdy, 2004. "News Arrival, Jump Dynamics, and Volatility Components for Individual Stock Returns," Journal of Finance, American Finance Association, vol. 59(2), pages 755-793, April.
    11. Liu, Cheng & Tang, Cheng Yong, 2014. "A quasi-maximum likelihood approach for integrated covariance matrix estimation with high frequency data," Journal of Econometrics, Elsevier, vol. 180(2), pages 217-232.
    12. Christophe Croux & Sébastien Laurent, 2011. "Outlyingness Weighted Covariation," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 9(4), pages 657-684.
    13. Bandi, Federico M. & Russell, Jeffrey R., 2006. "Separating microstructure noise from volatility," Journal of Financial Economics, Elsevier, vol. 79(3), pages 655-692, March.
    14. Zhang, Michael Yuanjie & Russell, Jeffrey R. & Tsay, Ruey S., 2008. "Determinants of bid and ask quotes and implications for the cost of trading," Journal of Empirical Finance, Elsevier, vol. 15(4), pages 656-678, September.
    15. Barry, Christopher B, 1974. "Portfolio Analysis under Uncertain Means, Variances, and Covariances," Journal of Finance, American Finance Association, vol. 29(2), pages 515-522, May.
    16. Fan, Jianqing & Wang, Yazhen, 2007. "Multi-Scale Jump and Volatility Analysis for High-Frequency Financial Data," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 1349-1362, December.
    17. Karpoff, Jonathan M., 1987. "The Relation between Price Changes and Trading Volume: A Survey," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 22(01), pages 109-126, March.
    18. Aït-Sahalia, Yacine & Fan, Jianqing & Xiu, Dacheng, 2010. "High-Frequency Covariance Estimates With Noisy and Asynchronous Financial Data," Journal of the American Statistical Association, American Statistical Association, vol. 105(492), pages 1504-1517.
    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:arx:papers:1602.02185. 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: (arXiv administrators)

    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.