Claudia Kirch

University of Karlsruhe, Germany

Bootstrapping sequential tests for change-point analysis

Change-point analysis studies whether the underlying model of an observed stochastic process changes at least once during the observational period. In a sequential setting we test the null hypothesis repeatedly after each new observation until a change is detected. This is specifically useful if data is collected automatically.

Critical values are usually based on distributional asymptotics, where the limit is taken with respect to a historic data set, which is used for model building. If this set is rather small the asymptotic distribution is not a good approximation.

Therefore we are interested in bootstrapping methods, which have been used extensively in classical testing but hardly at all in sequential situations. In such a setting we can make use of the new incoming observations for the bootstrap. From a practical point of view this is computationally expensive, so one needs some variations. From a theoretical point of view this means that we have new critical values with each incoming observation, so the question is whether this procedure remains consistent.