A UNIFIED MATHEMATICAL MODEL BRIDGING GENERATIVE ADVERSARIAL NETWORKS AND CENTURY-OLD STOCHASTIC THEORIES

Abstract

The utilization of generative adversarial networks (GANs) for the synthesizing of time-series data has gained increasing prominence in recent years, with applications extending across diverse domains such as financial modelling, music composition, and textual content analysis. Despite these advances, systematic evaluations contrasting GANs with alternative artificial intelligence (AI) methodologies or established mathematical frameworks remain relatively scarce. In this work, we undertake a comparative assessment of GANs against a canonical stochastic model, the Markov chain. Employing metrics derived from one- and two-point statistical analyses, we examine the capacity of each approach to replicate salient properties of time-series data. Our results indicate that, consistent with broader observations of AI-based generative models, GANs exhibit limitations in reproducing rare events and capturing cross-feature dependencies, thereby constraining their ability to generate fully faithful synthetic sequences. Although GANs demonstrate moderate proficiency in replicating auto-correlation structures, their performance remains markedly inferior to that of simple Markov chains. We further provide a qualitative discussion elucidating the structural reasons underlying these limitations, thereby contributing to a deeper understanding of the challenges inherent in AI-driven generative modelling of time-series data.