Testing stationarity in time series

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Abstract
We propose a procedure for testing stationarity of time series by combining a test for time independence of the 1D probability density with one of the spectral density. The potentials and limits of this test procedure are established by its application to different types of numerically generated time series ranging from simple linear stochastic processes to high-dimensional transient chaos as well as to observational data from geophysics and physiology. Problems of practical implementation are discussed, in particular the relation between the lengths of the time series and its maximal relevant time scales. Furthermore, artifacts and counterexamples are presented.