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Random noise arising from physical processes is an inherent characteristic ofmeasurements and a limiting factor for most signal processing and data analysistasks. Given the recent interest in generative adversarial networks (GANs) fordata-driven modeling, it is important to determine to what extent GANs canfaithfully reproduce noise in target data sets. In this paper, we present anempirical investigation that aims to shed light on this issue for time series.Namely, we assess two general-purpose GANs for time series that are based onthe popular deep convolutional GAN (DCGAN) architecture, a direct time-seriesmodel and an image-based model that uses a short-time Fourier transform (STFT)data representation. The GAN models are trained and quantitatively evaluatedusing distributions of simulated noise time series with known ground-truthparameters. Target time series distributions include a broad range of noisetypes commonly encountered in physical measurements, electronics, andcommunication systems: band-limited thermal noise, power law noise, shot noise,and impulsive noise. We find that GANs are capable of learning many noisetypes, although they predictably struggle when the GAN architecture is not wellsuited to some aspects of the noise, e.g., impulsive time-series with extremeoutliers. Our findings provide insights into the capabilities and potentiallimitations of current approaches to time-series GANs and highlight areas forfurther research. In addition, our battery of tests provides a useful benchmarkto aid the development of deep generative models for time series.

Data-Driven Modeling of Noise Time Series with Convolutional Generative Adversarial Networks