Minimax Optimality of CUSUM for an Autoregressive Model

Sven Knoth and Marianne Frisén
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Sven Knoth: Institute of Mathematics and Statistics, Helmut Schmidt University Hamburg, Postal: Institute of Mathematics and Statistics, Department of Economics and Social Sciences, Helmut Schmidt, University Hamburg, PO Box 700822, 22008 Hamburg,, Germany

No 2011:4, Research Reports from University of Gothenburg, Statistical Research Unit, School of Business, Economics and Law

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.

Keywords: Autoregressive; Change point; Monitoring; Online detection (search for similar items in EconPapers)
JEL-codes: C10 (search for similar items in EconPapers)
Pages: 27 pages
Date: 2011-02-10
New Economics Papers: this item is included in nep-ecm and nep-ets
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Citations: View citations in EconPapers (1)

Forthcoming as Knoth, Sven and Marianne Frisén, 'Minimax Optimality of CUSUM for an Autoregressive Model' in Statistica Neerlandica.

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Related works:
Journal Article: Minimax optimality of CUSUM for an autoregressive model (2012)
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