Surrogate data test for nonlinearity including nonmonotonic transforms

It is shown that monotonicity of the transform in the surrogate data test, which diminishes the applicability of the test, is not necessary and concerns only the prominent algorithm of amplitude adjusted Fourier transform (AAFT) for surrogate data generation. The failure of AAFT under nonmonotonicity is explained and a modified algorithm appropriate for nonmonotonic transforms, called corrected AAFT (CAAFT), is proposed. The superiority of CAAFT over AAFT is demonstrated with simulated and real data and compared also to the iterated AAFT algorithm.