IDEAS home Printed from https://ideas.repec.org/p/hhs/gunsru/2011_004.html
   My bibliography  Save this paper

Minimax Optimality of CUSUM for an Autoregressive Model

Author

Listed:
  • Knoth, Sven

    (Institute of Mathematics and Statistics, Helmut Schmidt University Hamburg)

  • Frisén, Marianne

    () (Statistical Research Unit, Department of Economics, School of Business, Economics and Law, Göteborg University)

Abstract

Different change point models for AR(1) processes are reviewed. For some models, the change is in the distribution conditional on earlier observations. For others the change is in the unconditional distribution. Some models include an observation before the first possible change time — others not. Earlier and new CUSUM type methods are given and minimax optimality is examined. For the conditional model with an observation before the possible change there are sharp results of optimality in the literature. The unconditional model with possible change at (or before) the first observation is of interest for applications. We examined this case and derived new variants of four earlier suggestions. By numerical methods and Monte Carlo simulations it was demonstrated that the new variants dominate the original ones. However, none of the methods is uniformly minimax optimal.

Suggested Citation

  • Knoth, Sven & Frisén, Marianne, 2011. "Minimax Optimality of CUSUM for an Autoregressive Model," Research Reports 2011:4, University of Gothenburg, Statistical Research Unit, School of Business, Economics and Law.
  • Handle: RePEc:hhs:gunsru:2011_004
    as

    Download full text from publisher

    File URL: http://gup.ub.gu.se/records/fulltext/136688.pdf
    Download Restriction: no

    Other versions of this item:

    Citations

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


    Cited by:

    1. Liubov Rabyk & Wolfgang Schmid, 2016. "EWMA control charts for detecting changes in the mean of a long-memory process," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 79(3), pages 267-301, April.
    2. Robert Garthoff & Iryna Okhrin & Wolfgang Schmid, 2014. "Statistical surveillance of the mean vector and the covariance matrix of nonlinear time series," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 98(3), pages 225-255, July.

    More about this item

    Keywords

    Autoregressive; Change point; Monitoring; Online detection;

    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General

    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:hhs:gunsru:2011_004. 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: (Linus Schiöler). General contact details of provider: http://www.statistics.gu.se/ .

    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 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.

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.