Impact of extremely heavy tails on training and performance of deep generative time-series models

Determine whether the very heavy tails of an AR(1)+GARCH process with t(3) innovations causally disrupt the training and degrade the performance of deep generative time-series models used in the study, such as Conditional WGAN, CGAN with fully connected layers, Conditional TimeVAE, and Signature CWGAN, and characterize the extent of this effect.

Background

The authors evaluate multiple models on data simulated from AR(1)+GARCH processes with various innovation distributions. When the innovations follow a t(3) distribution, performance rankings differ notably from other cases, suggesting potential instability or degradation in model training or inference under extremely heavy-tailed conditions.

They explicitly advance a conjecture that the pronounced fat tails may be responsible for the observed issues, but do not establish this formally, leaving open the task of verifying and quantifying the effect across the tested deep generative architectures.