View Submission - COMPSTAT2022

A0151
**Title: **Are deviations in a gradually varying mean relevant?
**Authors: **Holger Dette - Ruhr-Universitaet Bochum (Germany) **[presenting]**

**Abstract: **Classical change point analysis aims at (1) detecting abrupt changes in the mean of a possibly non-stationary time series and at (2) identifying regions where the mean exhibits a piecewise constant behaviour. In many applications (for example climatology) however, it is more reasonable to assume that the mean changes gradually in a smooth way. Those gradual changes may either be non-relevant (i.e., small), or relevant for a specific problem at hand. We develop a statistical methodology to detect the latter. More precisely, we consider a locally stationary process with a time-varying trend and propose a test for the null hypothesis that the maximum absolute deviation of the trend from a given benchmark (such as the value of the trend at the beginning of the observation period or an average value over the past) is smaller than a given threshold. A test for this type of hypothesis is developed using an appropriate estimator for the maximum deviation. We also provide estimates for the time point, where this relevant deviation appears for the first time.