^{1}

^{1}

^{1}

A stochastic version of the Iterative Amplitude Adjusted Fourier Transform (IAAFT) algorithm is presented. This algorithm is able to generate so-called surrogate time series, which have the amplitude distribution and the power spectrum of measured time series or fields. The key difference between the new algorithm and the original IAAFT method is the treatment of the amplitude adjustment: it is not performed for all values in each iterative step, but only for a fraction of the values. This new algorithm achieves a better accuracy, i.e. the power spectra of the measurement and its surrogate are more similar. We demonstrate the improvement by applying the IAAFT algorithm and the new one to 13 different test signals ranging from rain time series and 3-dimensional clouds to fractal time series and theoretical input. The improved accuracy can be important for generating high-quality geophysical time series and fields. The traditional application of the IAAFT algorithm is statistical nonlinearity testing. Reassuringly, we found that in most cases the accuracy of the original IAAFT algorithm is sufficient for this application.