IDEAS home Printed from https://ideas.repec.org/a/bla/jtsera/v21y2000i1p33-59.html
   My bibliography  Save this article

Least‐squares Estimation of an Unknown Number of Shifts in a Time Series

Author

Listed:
  • Marc Lavielle
  • Eric Moulines

Abstract

In this contribution, general results on the off‐line least‐squares estimate of changes in the mean of a random process are presented. First, a generalisation of the Hajek‐Renyi inequality, dealing with the fluctuations of the normalized partial sums, is given. This preliminary result is then used to derive the consistency and the rate of convergence of the change‐points estimate, in the situation where the number of changes is known. Strong consistency is obtained under some mixing conditions. The limiting distribution is also computed under an invariance principle. The case where the number of changes is unknown is then addressed. All these results apply to a large class of dependent processes, including strongly mixing and also long‐range dependent processes.

Suggested Citation

  • Marc Lavielle & Eric Moulines, 2000. "Least‐squares Estimation of an Unknown Number of Shifts in a Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 21(1), pages 33-59, January.
  • Handle: RePEc:bla:jtsera:v:21:y:2000:i:1:p:33-59
    DOI: 10.1111/1467-9892.00172
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/1467-9892.00172
    Download Restriction: no

    File URL: https://libkey.io/10.1111/1467-9892.00172?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
    ---><---

    More about this item

    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:bla:jtsera:v:21:y:2000:i:1:p:33-59. 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: Wiley Content Delivery (email available below). General contact details of provider: http://www.blackwellpublishing.com/journal.asp?ref=0143-9782 .

    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.