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

TL;DR

This paper introduces a Fourier transform-based method for generating synthetic time series data that closely mimics the statistical properties of original signals, with controllable similarity levels, applicable across various environmental datasets.

Contribution

The paper presents a novel Fourier transform-based approach that preserves key statistical moments and autocorrelation, offering a flexible and general method for synthetic time series generation.

Findings

Method preserves first two statistical moments.

Method maintains autocorrelation structure.

Outperforms ARMA, GAN, and CoSMoS in tests.

Abstract

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 robustness. 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. This paper presents 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 signals. 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 environmental 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.