Saturation in Autoregressive Models

In this paper, we extend the impulse saturation algorithm to a class of dynamic models. We show that the procedure is still correctly sized for stationary AR(1) processes, independently of the number of splits used for sample partitions. We derive theoretical power when there is an additive outlier in the data, and present simulation evidence showing good empirical rejection frequencies against such an alternative. Extensive Monte Carlo evidence is presented to document that the procedure has good power against a level shift in the last rT% of the sample observations. This result does not depend on the level of serial correlation of the data and does not require the use of a (mis-specified) location-scale model, thus opening the door to an automatic class of break tests that could outperform those of the Bai-Perron type.