Synthesizing water-related time series for simulation studies while maintaining the original signal’s statistical moments

In many studies arises the need to generate synthetic data sets. Such data can answer different needs as data imputation, non-stationary systems analysis, Monte Carlo simulations, training of data-driven models, uncertainty analysis and more. Previous efforts to generate synthetic data focused mostly on statistical methods which did not maintain the statistical moments of the original dataset, while producing a large number of random different time series. Here, a novel method is developed, based on signal processing and discrete Fourier transform (DFT) theory. The method allows to generate synthetic time series signals with similar statistical moments of any given signal. Moreover, the method allows control on the correlation level between the original and the synthesized signals. We also provide mathematical proofs that our method maintains the first two statistical moments. The method is illustrated on two different datasets showing that also the third and fourth moments are kept. Figure 1 shows, in blue, a true water demand time-series taken from a real-life system. For this signal, 50 synthesized signals are generated with increasing correlation levels - from top, with the lowest correlation, to bottom, presenting the highest correlations between the original and synthesized signals.

                                                                                                                    

                                                                Figure 1 – Domestic water demand signal with different correlation level