Authors: Heinrichs, Florian
Dette, Holger
Title: A distribution free test for changes in the trend function of locally stationary processes
Language (ISO): en
Abstract: In the common time series model Xi,n = μ(i/n)+"i,n with non-stationary errors we consider the problem of detecting a significant deviation of the mean function g(μ) from a benchmark g(μ) (such as the initial value μ(0) or the average trend R 1 0 μ(t)dt). The problem is motivated by a more realistic modelling of change point analysis, where one is interested 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 appropriate 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.
Subject Headings: change point analysis
nonparametric regression
nonparametric regression
Issue Date: 2020
Appears in Collections:Sonderforschungsbereich (SFB) 823

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