Test your surrogate data before you test for nonlinearity
Abstract
The schemes for the generation of surrogate data in order to test the null hypothesis of linear stochastic process undergoing nonlinear static transform are investigated as to their consistency in representing the null hypothesis. In particular, we pinpoint some important caveats of the prominent algorithm of amplitude adjusted Fourier transform surrogates (AAFT) and compare it to the iterated AAFT, which is more consistent in representing the null hypothesis. It turns out that in many applications with real data the inferences of nonlinearity after marginal rejection of the null hypothesis were premature and have to be reinvestigated taking into account the inaccuracies 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 wellknown real data sets cautions against the use of the AAFT algorithm.
 Publication:

Physical Review E
 Pub Date:
 September 1999
 DOI:
 10.1103/PhysRevE.60.2808
 arXiv:
 arXiv:physics/9905021
 Bibcode:
 1999PhRvE..60.2808K
 Keywords:

 05.45.Tp;
 05.10.Ln;
 Time series analysis;
 Monte Carlo methods;
 Physics  Data Analysis;
 Statistics and Probability;
 Physics  Computational Physics
 EPrint:
 14 pages, 15 figures, submitted to Physical Review E