Monitoring changes in linear models

Abstract We propose two classes of monitoring schemes to (sequentially) detect a structural change in a linear model after a training period of size m. The first class of procedures is based on weighted CUSUMs of residuals, in which the unknown in-control parameter has been replaced by its least-squares estimate from the training sample, whereas the second class of schemes makes use of the CUSUMs of recursive residuals. The weight function can be chosen in a flexible way according to whether an early or late change after time m is expected. The procedures are designed so that the tests have a small probability of a false alarm (as m→∞) and asymptotic power one. A small simulation study illustrates the finite sample performance of the monitoring schemes for various choices of weight functions.

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