Sequential Change-Point Analysis based on Invariance Principles

Change-point analysis is concerned with detecting structural breaks of stochastic processes based on a (longer) series of observations. In this dissertation, we derive (nonparametric) sequential test procedures that take into account new motivation coming from econometrics. The main basis for the proofs are invariance principles which allow to reduce the statistical analysis to investigating the properties of the limit process. Taking into account results for linear models, a location model is introduced to test for possible changes in the mean of underlying random variables. Therein, we examine the asymptotic behaviour of the test procedure under both hypotheses and obtain the limit distribution of the corresponding stopping time. In a second part, so-called RCA(1) time series are studied. It turns out that these processes satisfy a strong invariance principle with a certain rate. This allows for retaining the previous results. Moreover, a-posteriori tests are provided to examine the stability of a model parameter. Finally, we discuss the behaviour of suprema of stochastic processes with linear drift. The results obtained can be utilized to construct sequential tests in multivariate settings