Synthetic random environmental time series generation with similarity control, preserving original signal's statistical characteristics

Synthetic datasets are widely used in applications like missing data imputation, simulations, training data-driven models, and system robustness analysis. Typically based on historical data, these datasets need to represent specific system behaviors while being diverse enough to challenge the system with a broad range of inputs. This paper introduces a method using discrete Fourier transform to generate synthetic time series with similar statistical moments to any given signal. The method allows control over the similarity level between the original and synthetic signals. Analytical proof shows that this method preserves the first two statistical moments and the autocorrelation function of the input signal. It is compared to ARMA, GAN, and CoSMoS methods using various environmental datasets with different temporal resolutions and domains, demonstrating its generality and flexibility. A Python library implementing this method is available as open-source software.