## Publications

### A distribution free test for changes in the trend function of locally stationary processes∗

Heinrichs, F. and Dette, H.

**ELECTRONIC JOURNAL OF STATISTICS****Volume:** 15 **Pages:** 3762-3797**DOI: **10.1214/21-EJS1871**Published: ** 2021

Abstract

In the common time series model Xi,n = μ(i/n) +εi,n with non-stationary errors we consider the problem of detecting a significant deviation of the mean function μ from a benchmark g(μ) (suchastheini-tial value μ(0) or the average trend∫ 1 0 μ(t)dt). The problem is motivated by a more realistic modelling of change point analysis, where one is inter-ested in identifying relevant deviations in a smoothly varying sequence of means (μ(i/n))i=1,…,n and cannot assume that the sequence is piecewise constant. A test for this type of hypotheses is developed using an appro-priate estimator for the integrated squared deviation of the mean function and the threshold. By a new concept of self-normalization adapted to non-stationary processes an asymptotically pivotal test for the hypothesis of a relevant deviation is constructed. The results are illustrated by means of a simulation study and a data example. © 2021, Institute of Mathematical Statistics. All rights reserved.