Dette, HolgerPreuß, PhilipSen, Kemal2013-03-142013-03-142013-03-14http://hdl.handle.net/2003/3009710.17877/DE290R-10344In this paper we consider the problem of measuring stationarity in locally stationary longmemory processes. We introduce an L2-distance between the spectral density of the locally stationary process and its best approximation under the assumption of stationarity. The distance is estimated by a numerical approximation of the integrated spectral periodogram and asymptotic normality of the resulting estimate is established. The results can be used to construct a simple test for the hypothesis of stationarity in locally stationary long-range dependent processes. We also propose a bootstrap procedure to improve the approximation of the nominal level and prove its consistency. Throughout the paper, we will work with Riemann sums of a squared periodogram instead of integrals (as it is usually done in the literature) and as a byproduct of independent interest it is demonstrated that the two approaches behave differently in the limit.enDiscussion Paper / SFB 823;9/2013bootstrapempirical spectral measuregoodness-of-fit testsintegrated periodogramlocally stationary processlong-memorynon-stationary processesspectral density310330620working paper