Surrogate testing of linear feedback processes with non-Gaussian innovations

TL;DR

This paper evaluates the effectiveness of different surrogate testing methods in identifying linear feedback processes with non-Gaussian innovations, highlighting limitations of existing procedures in such contexts.

Contribution

It analyzes the applicability of phase-randomized, AAFT, and IAAFT surrogates for non-Gaussian innovations, revealing their limitations in certain nonlinear and non-Gaussian scenarios.

Findings

Phase-randomized surrogates may not be suitable for non-Gaussian innovations.

AAFT and IAAFT surrogates have limitations with static nonlinear transforms.

Existing surrogate methods may fail to accurately infer process nature with non-Gaussian noise.

Abstract

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 (AAFT) and iterated amplitude adjusted Fourier transform (IAAFT) surrogates on statistical inference of linearly correlated noise with non-Gaussian innovations and their static, invertible nonlinear transforms from their empirical samples is 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.