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

Wiener-Kolmogorov Filtering and Smoothing for Multivariate Series With State-Space Structure

  • Víctor Gómez
Registered author(s):

    Wiener-Kolmogorov filtering and smoothing usually deal with projection problems for stochastic processes that are observed over semi-infinite and doubly infinite intervals. For multivariate stationary series, there exist closed formulae based on covariance generating functions that were first given independently by N. Wiener and A.N. Kolmogorov around 1940. In this article, we consider multivariate series with a state-space structure and, using a new purely algebraic approach to the problem, we prove the equivalence between Wiener-Kolmogorov filtering and Kalman filtering. Up to now, this equivalence has only been partially shown. In addition, we get some new recursions for smoothing and some new recursions to compute the filter weights and the covariance generating functions of the errors. The results are extended to nonstationary series. Copyright 2007 The Author Journal compilation 2007 Blackwell Publishing Ltd.

    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.blackwell-synergy.com/doi/abs/10.1111/j.1467-9892.2006.00514.x
    File Function: link to full text
    Download Restriction: Access to full text is restricted to subscribers.

    As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.

    Article provided by Wiley Blackwell in its journal Journal of Time Series Analysis.

    Volume (Year): 28 (2007)
    Issue (Month): 3 (05)
    Pages: 361-385

    as
    in new window

    Handle: RePEc:bla:jtsera:v:28:y:2007:i:3:p:361-385
    Contact details of provider: Web page: http://www.blackwellpublishing.com/journal.asp?ref=0143-9782

    Order Information: Web: http://www.blackwellpublishing.com/subs.asp?ref=0143-9782

    No references listed on IDEAS
    You can help add them by filling out this form.

    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:bla:jtsera:v:28:y:2007:i:3:p:361-385. 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: (Wiley-Blackwell Digital Licensing)

    or (Christopher F. Baum)

    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.