Minimax optimality of CUSUM for an autoregressive model |
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Authors: | Sven Knoth Marianne Frisén |
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Affiliation: | 1. Department of Economics and Social Sciences, Institute of Mathematics and Statistics, Helmut Schmidt University Hamburg, P. O. Box 700822, 22008 Hamburg, Germany;2. Department of Economics, Statistical Research Unit, University of Gothenburg, Box 640, SE 405 30 G?teborg, Sweden |
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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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Keywords: | autoregressive change point monitoring online detection |
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