IDEAS home Printed from https://ideas.repec.org/p/eca/wpaper/2013-241623.html
   My bibliography  Save this paper

Asymptotic Properties of QML Estimators for VARMA Models with Time-Dependent Coefficients

Author

Listed:
  • Abdelkamel Alj
  • Rajae Azrak
  • Christophe Ley
  • Guy Melard

Abstract

This paper is about vector autoregressive-moving average (VARMA) models with time-dependent coefficients to represent non-stationary time series. Contrary to other papers in the univariate case, the coefficients depend on time but not on the series’ length n. Under appropriate assumptions, it is shown that a Gaussian quasi-maximum likelihood estimator is almost surely consistent and asymptotically normal. The theoretical results are illustrated by means of two examples of bivariate processes. It is shown that the assumptions underly- ing the theoretical results apply. In the second example the innovations are marginally heteroscedastic with a correlation ranging from −0.8 to 0.8. In the two examples, the asymptotic information matrix is obtained in the Gaussian case. Finally, the finite-sample behavior is checked via a Monte Carlo simulation study for n from 25 to 400. The results confirm the validity of the asymptotic properties even for short series and the asymptotic information matrix deduced from the theory.

Suggested Citation

  • Abdelkamel Alj & Rajae Azrak & Christophe Ley & Guy Melard, 2016. "Asymptotic Properties of QML Estimators for VARMA Models with Time-Dependent Coefficients," Working Papers ECARES ECARES 2016-41, ULB -- Universite Libre de Bruxelles.
  • Handle: RePEc:eca:wpaper:2013/241623
    as

    Download full text from publisher

    File URL: https://dipot.ulb.ac.be/dspace/bitstream/2013/241623/3/2016-41-ALJ_AZRAK_LEY_MELARD-asymptotic.pdf
    File Function: Full text for the whole work, or for a work part
    Download Restriction: no
    ---><---

    Citations

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


    Cited by:

    1. Abdelkamel Alj & Rajae Azrak & Christophe Ley & Guy Melard, 2016. "Technical Appendix to Asymptotic Properties of QML Estimators for VARMA Models with Time-Dependent Coefficients," Working Papers ECARES ECARES 2016-42, ULB -- Universite Libre de Bruxelles.

    More about this item

    Keywords

    non-stationary process; multivariate time series; time-varying models;
    All these keywords.

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    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:eca:wpaper:2013/241623. 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: Benoit Pauwels (email available below). General contact details of provider: https://edirc.repec.org/data/arulbbe.html .

    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.