This paper introduces an improved method for generating surrogate data to test for nonlinearity in time series. The traditional approach compares a time series to a null hypothesis of a Gaussian linear stochastic process, but this is too restrictive. The authors propose a more general null hypothesis that allows for nonlinear rescalings of a Gaussian linear process. They show that simple amplitude adjustments of surrogates can lead to spurious detection of nonlinearity. An iterative algorithm is proposed to generate surrogates that have the same autocorrelations and probability distribution as the data. The authors argue that the null hypothesis of deterministic chaos is attractive for studying irregular time evolution, but nonlinear algorithms can mistakenly identify linear correlations as determinism. They propose testing results against a specific class of linear random processes. The method of "surrogate data" is used, which involves comparing a nonlinear statistic to its empirical distribution on Monte Carlo realizations of the null hypothesis. The authors propose an algorithm called the amplitude adjusted Fourier transform (AAFT) to test this null hypothesis. The data is first rendered Gaussian by rank-ordering according to a set of Gaussian random numbers. The resulting series is then phase randomized, and finally, the rescaling is inverted to match the original data distribution. However, the AAFT algorithm can introduce systematic errors in the empirical power spectrum, leading to false rejections of the null hypothesis. The authors propose an alternative method that uses an iterative scheme to generate surrogates with the same power spectrum and distribution as the data. This method involves sorting the data and iteratively adjusting the phases of the Fourier transform to match the desired spectrum. The algorithm is tested on various data sets, and it is shown that the number of false rejections can be significantly reduced by increasing the number of iterations. The authors conclude that their algorithm provides a more accurate method for generating surrogate data with the same power spectrum and distribution as the data. The accuracy of the algorithm depends on the nature of the data and the length of the time series. The method is particularly effective for data with strong correlations, although the rate of convergence depends on the distribution of the data and the nature of the correlations. The authors also note that the rejection of the null hypothesis does not necessarily imply nonlinear dynamics, as some linear processes can lead to the rejection of the null hypothesis.This paper introduces an improved method for generating surrogate data to test for nonlinearity in time series. The traditional approach compares a time series to a null hypothesis of a Gaussian linear stochastic process, but this is too restrictive. The authors propose a more general null hypothesis that allows for nonlinear rescalings of a Gaussian linear process. They show that simple amplitude adjustments of surrogates can lead to spurious detection of nonlinearity. An iterative algorithm is proposed to generate surrogates that have the same autocorrelations and probability distribution as the data. The authors argue that the null hypothesis of deterministic chaos is attractive for studying irregular time evolution, but nonlinear algorithms can mistakenly identify linear correlations as determinism. They propose testing results against a specific class of linear random processes. The method of "surrogate data" is used, which involves comparing a nonlinear statistic to its empirical distribution on Monte Carlo realizations of the null hypothesis. The authors propose an algorithm called the amplitude adjusted Fourier transform (AAFT) to test this null hypothesis. The data is first rendered Gaussian by rank-ordering according to a set of Gaussian random numbers. The resulting series is then phase randomized, and finally, the rescaling is inverted to match the original data distribution. However, the AAFT algorithm can introduce systematic errors in the empirical power spectrum, leading to false rejections of the null hypothesis. The authors propose an alternative method that uses an iterative scheme to generate surrogates with the same power spectrum and distribution as the data. This method involves sorting the data and iteratively adjusting the phases of the Fourier transform to match the desired spectrum. The algorithm is tested on various data sets, and it is shown that the number of false rejections can be significantly reduced by increasing the number of iterations. The authors conclude that their algorithm provides a more accurate method for generating surrogate data with the same power spectrum and distribution as the data. The accuracy of the algorithm depends on the nature of the data and the length of the time series. The method is particularly effective for data with strong correlations, although the rate of convergence depends on the distribution of the data and the nature of the correlations. The authors also note that the rejection of the null hypothesis does not necessarily imply nonlinear dynamics, as some linear processes can lead to the rejection of the null hypothesis.