Synthetic Random Environmental Time Series Generation with Similarity Control, Preserving Original Signal's Statistical Characteristics

Abstract Submission: Synthetic datasets are widely used in many applications, such as missing data imputation, examining
non-stationary scenarios, in simulations, training data-driven models, and analyzing system robust-
ness. Typically, synthetic data are based on historical data obtained from the observed system. The
data needs to represent a specific behavior of the system, yet be new and diverse enough so that
the system is challenged with a broad range of inputs. Here we present a method, based on
discrete Fourier transform, for generating synthetic time series with similar statistical moments for
any given signal. The suggested method makes it possible to control the level of similarity between
the given signal and the generated synthetic ones. Proof shows analytically that this method
preserves the first two statistical moments of the input signal, and its autocorrelation function. The
method is compared to known methods, ARMA, GAN, and CoSMoS. A large variety of environ-
mental datasets with different temporal resolutions, and from different domains are used, testing
the generality and flexibility of the method. A Python library implementing this method is made
available as open-source software.

Learning Objectives/Expected Outcome (Optional) :