Scandinavian Working Papers in Economics
Research Reports,
University of Gothenburg, Statistical Research Unit, School of Business, Economics and Law
No 2011:4: Minimax Optimality of CUSUM for an Autoregressive Model
Sven Knoth and Marianne Frisén ()
Additional contact information
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
Marianne Frisén: Statistical Research Unit, Department of Economics, School of Business, Economics and Law, Göteborg University, Postal: Statistical Research Unit, Göteborg University, Box 640, SE 40530 GÖTEBORG
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
JEL-codes: C10
27 pages, February 10, 2011
Full text files
136688.pdf
- Fortchoming as
- Sven Knoth and Marianne Frisén, 'Minimax Optimality of CUSUM for an Autoregressive Model', Statistica Neerlandica
- University of Gothenburg, Statistical Research Unit, School of Business, Economics and Law
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