On the detection of changes in autoregressive time series I. Asymptotics

Various test statistics are discussed which can be used for detecting changes in the parameters of an autoregressive time series. In this first part of our study, the limiting behavior of the test statistics is derived under the null hypothesis of no change as well as under alternatives. In a forthcoming second part of our investigation, these asymptotic results will be compared to some corresponding bootstrap procedures, and a small simulation study will be conducted.