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Minimax optimality of CUSUM for an autoregressive model

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  • Sven Knoth
  • Marianne Frisén

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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Suggested Citation

  • Sven Knoth & Marianne Frisén, 2012. "Minimax optimality of CUSUM for an autoregressive model," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 66(4), pages 357-379, November.
    • Handle: RePEc:bla:stanee:v:66:y:2012:i:4:p:357-379
    DOI: j.1467-9574.2012.00512.x
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    Cited by:

    1. Taras Lazariv & Wolfgang Schmid, 2019. "Surveillance of non-stationary processes," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 103(3), pages 305-331, September.
    2. Frisén, Marianne, 2011. "Inference Principles For Multivariate Surveillance," Research Reports 2011:5, University of Gothenburg, Statistical Research Unit, School of Business, Economics and Law.
    3. 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.

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    JEL classification:

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

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