The paper by Thomas Schreiber and Andreas Schmitz proposes an improved method for generating surrogate data to test for nonlinearity in time series. Current tests often compare a time series to the null hypothesis of a Gaussian linear stochastic process, but this can lead to false positives due to the inability to account for nonlinear rescalings. The authors introduce a more general null hypothesis that allows for nonlinear rescalings of a Gaussian linear process. They propose an iterative algorithm to create surrogates that have the same autocorrelations and probability distribution as the original data, ensuring that the surrogates do not introduce spurious nonlinearity. The algorithm involves sorting the data, adjusting the power spectrum, and reordering the values to match the original data. The effectiveness of the algorithm is demonstrated through simulations, showing that it reduces false rejections of the null hypothesis compared to the amplitude-adjusted Fourier transform (AAFT) method. The paper also discusses the limitations and potential issues with the proposed method, such as the possibility of introducing spurious structure in the surrogates.The paper by Thomas Schreiber and Andreas Schmitz proposes an improved method for generating surrogate data to test for nonlinearity in time series. Current tests often compare a time series to the null hypothesis of a Gaussian linear stochastic process, but this can lead to false positives due to the inability to account for nonlinear rescalings. The authors introduce a more general null hypothesis that allows for nonlinear rescalings of a Gaussian linear process. They propose an iterative algorithm to create surrogates that have the same autocorrelations and probability distribution as the original data, ensuring that the surrogates do not introduce spurious nonlinearity. The algorithm involves sorting the data, adjusting the power spectrum, and reordering the values to match the original data. The effectiveness of the algorithm is demonstrated through simulations, showing that it reduces false rejections of the null hypothesis compared to the amplitude-adjusted Fourier transform (AAFT) method. The paper also discusses the limitations and potential issues with the proposed method, such as the possibility of introducing spurious structure in the surrogates.