IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v176y2020ics0047259x19301654.html
   My bibliography  Save this article

Closed-form expression for finite predictor coefficients of multivariate ARMA processes

Author

Listed:
  • Inoue, Akihiko

Abstract

We derive a closed-form expression for the finite predictor coefficients of multivariate ARMA (autoregressive moving-average) processes. The expression is given in terms of several explicit matrices that are of fixed sizes independent of the number of observations. The significance of the expression is that it provides us with a linear-time algorithm to compute the finite predictor coefficients. In the proof of the expression, a correspondence result between two relevant matrix-valued outer functions plays a key role. We apply the expression to determine the asymptotic behavior of a sum that appears in the autoregressive model fitting and the autoregressive sieve bootstrap. The results are new even for univariate ARMA processes.

Suggested Citation

  • Inoue, Akihiko, 2020. "Closed-form expression for finite predictor coefficients of multivariate ARMA processes," Journal of Multivariate Analysis, Elsevier, vol. 176(C).
    • Handle: RePEc:eee:jmvana:v:176:y:2020:i:c:s0047259x19301654
    DOI: 10.1016/j.jmva.2019.104578
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047259X19301654
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jmva.2019.104578?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Tucker S. McElroy & Dimitris N. Politis, 2022. "Optimal linear interpolation of multiple missing values," Statistical Inference for Stochastic Processes, Springer, vol. 25(3), pages 471-483, October.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:jmvana:v:176:y:2020:i:c:s0047259x19301654. See general information about how to correct material in RePEc.

    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.

    We have no bibliographic references for this item. You can help adding them by using 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 RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

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

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.