It is shown that the test has asymptotic power one for a wide range of alternatives not restricted to changes in the mean of the time series. Furthermore, we prove that the corresponding estimator converges to the true change point with the optimal rate and derive the asymptotic distribution. Some simulations illustrate the behavior of the estimator with a special focus on the misspecified case, where the regression function is indeed not given by a neuronal network. Finally, we apply the estimator to some financial data.
Kooperationen: Dr. Stefanie Schwaar, ITWM Kaiserslautern