  Random noise arising from physical processes is an inherent characteristic of
measurements and a limiting factor for most signal processing and data analysis
tasks. Given the recent interest in generative adversarial networks (GANs) for
data-driven modeling, it is important to determine to what extent GANs can
faithfully reproduce noise in target data sets. In this paper, we present an
empirical 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 on
the popular deep convolutional GAN (DCGAN) architecture, a direct time-series
model and an image-based model that uses a short-time Fourier transform (STFT)
data representation. The GAN models are trained and quantitatively evaluated
using distributions of simulated noise time series with known ground-truth
parameters. Target time series distributions include a broad range of noise
types commonly encountered in physical measurements, electronics, and
communication systems: band-limited thermal noise, power law noise, shot noise,
and impulsive noise. We find that GANs are capable of learning many noise
types, although they predictably struggle when the GAN architecture is not well
suited to some aspects of the noise, e.g., impulsive time-series with extreme
outliers. Our findings provide insights into the capabilities and potential
limitations of current approaches to time-series GANs and highlight areas for
further research. In addition, our battery of tests provides a useful benchmark
to aid the development of deep generative models for time series.
