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Minimax Optimality of CUSUM for an Autoregressive Model

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Author Info

  • 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.

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Bibliographic Info

Paper provided by Statistical Research Unit, Department of Economics, School of Business, Economics and Law, University of Gothenburg in its series Research Reports with number 2011:4.

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Length: 27 pages
Date of creation: 10 Feb 2011
Date of revision:
Publication status: Forthcoming as Knoth, Sven and Marianne Frisén, 'Minimax Optimality of CUSUM for an Autoregressive Model' in Statistica Neerlandica.
Handle: RePEc:hhs:gunsru:2011_004

Contact details of provider:
Postal: Statistical Research Unit, University of Gothenburg, Box 640, SE 40530 GÖTEBORG
Web page: http://www.statistics.gu.se/

Related research

Keywords: Autoregressive; Change point; Monitoring; Online detection;

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