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Delay time in monitoring jump changes in linear models

Along the lines of Hušková and Koubková [Sequential procedures for detection of changes in autoregressive sequences, in Proceedings of Prague Stochastics 2006, M. Hušková and M. Janžura, eds., MatfyzPress, Charles University, Prague, pp. 437–447], we further investigate a sequential procedure for monitoring jump changes in linear models. Our main result shows that, under the alternative, the suitably normalized stopping time of the procedure has a standard normal limiting distribution. A number of examples are discussed and the finite sample validity of the asymptotics is checked via a small simulation study.