Bootstrap Change Point Testing for Dependent Data

Abstract

Critical values of change point tests in location and regression models are usually based on limit distribution of the respective test statistics under the null hypothesis. However, the limit distribution is very often a functional of some Gaussian processes depending on unknown quantities that cannot be easily estimated. In many situations, convergence to the asymptotic distribution is rather slow and the asymptotic critical values are not well applicable in small and moderate samples. It has appeared that resampling methods provide reasonable approximations for critical values of test statistics for detection changes in location and regression models. In this chapter dependent wild bootstrap procedure for testing changes in linear model with weakly dependent regressors and errors will be proposed and its validity verified. More specifically, the concept of \(L_p\)-m-approximability will be used.