Surrogate testing of linear feedback processes with non-Gaussian innovations

Surrogate testing is used widely to determine the nature of the process generating the given empirical sample. In the present study, the usefulness of phase-randomized surrogates, amplitude adjusted Fourier transform and iterated amplitude adjusted Fourier transform surrogates on statistical inference of linearly correlated noise with non-Gaussian innovations and their static, invertible nonlinear transforms from their empirical samples are discussed. Existing surrogate testing procedures, which retain the auto-correlation function in the surrogates, may not be appropriate in the presence of non-Gaussian innovations.