  The method of surrogates is one of the key concepts of nonlinear data
analysis. Here, we demonstrate that commonly used algorithms for generating
surrogates often fail to generate truly linear time series. Rather, they create
surrogate realizations with Fourier phase correlations leading to
non-detections of nonlinearities. We argue that reliable surrogates can only be
generated, if one tests separately for static and dynamic nonlinearities.
