Test your surrogate data before you test for nonlinearity

The schemes for the generation of surrogate data in order to test the null hypothesis of linear stochastic process undergoing nonlinear static transfo rm are investigated as to their consistency in representing the null hypoth esis. In particular, we pinpoint some important caveats of the prominent al gorithm of amplitude adjusted Fourier transform surrogates (AAFT) and compa re it to the iterated AAFT, which is more consistent in representing the nu ll hypothesis. It turns out that in many applications with real data the in ferences of nonlinearity after marginal rejection of the null hypothesis we re premature and have to be reinvestigated taking into account the inaccura cies in the AAFT algorithm, mainly concerning the mismatching of the linear correlations. In order to deal with such inaccuracies, we propose the use of linear together with nonlinear polynomials as discriminating statistics. The application of this setup to some well-known real data sets cautions a gainst the use of the AAFT algorithm. [S1063-651X(99)02509-X].