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

In the common time series model Xi,n=μ(i∕n)+εi,n with non-stationary errors we consider problem of detecting a significant deviation mean function μ from benchmark g(μ) (such as initial value μ(0) or average trend ∫01μ(t)dt). The is motivated by more realistic modelling change point analysis, where one interested in identifying relevant deviations smoothly varying sequence means (μ(i∕n))i=1,…,n and cannot assume that piecewise constant. A test for this type hypotheses developed using an appropriate estimator integrated squared threshold. By new concept self-normalization adapted to processes asymptotically pivotal hypothesis constructed. results are illustrated simulation study data example.