  To understand the ability and limitations of convolutional neural networks to
generate time series that mimic complex temporal signals, we trained a
generative adversarial network consisting of deep convolutional networks to
generate chaotic time series and used nonlinear time series analysis to
evaluate the generated time series. A numerical measure of determinism and the
Lyapunov exponent, a measure of trajectory instability, showed that the
generated time series well reproduce the chaotic properties of the original
time series. However, error distribution analyses showed that large errors
appeared at a low but non-negligible rate. Such errors would not be expected if
the distribution were assumed to be exponential.
