Are Deviations in a Gradually Varying Mean Relevant? a Testing Approach Based on Sup-Norm Estimators

• Activity Number: 118 - Recent Advances in Change-Point Analysis
• Type: Invited
• Date/Time: Monday, August 8, 2022 : 10:30 AM to 12:20 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Holger Dette* and Axel Bücher and Florian Heinrichs
• Companies: Ruhr University Bochum and Heinrich Heine University Düsseldorf and Ruhr-Universität Bochum
• Keywords: local stationarity; relevant change point; Gumbel distribution; gradual changes

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 behavior. In many applications 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, and the present paper presents 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) is smaller than a given threshold. A test for this type of hypotheses is developed using an appropriate estimator for the maximum deviation. We derive the limiting distribution of a standardized version of this estimator and illustrate the final sample properties of the test by means of a simulation study and a data example.