Modern AI versus century-old mathematical models: How far can we go with generative adversarial networks to reproduce stochastic processes?

Abstract

The usage of generative adversarial networks (GAN)s for synthetic time-series data generation has been gaining popularity in recent years with applications from finance to music composition and processing of textual content. However, beyond their reported success, few comparisons exist with other artificial intelligence (AI) methods or standard mathematical models. Here, we test GANs performance, comparing them with a well-known mathematical model, namely a Markov chain. We implement comparative metrics based on one- and two-point statistics to evaluate the performance of each method. We find that, similarly to other AI approaches, GANs struggle to capture rare events and cross-feature relations and are unable to create synthetic faithful data. GANs are relatively successful in replicating the auto-correlation function, but they still lag significantly behind simple Markov chains. We also provide a qualitative explanation for this limitation of AI approaches.