Title: Synthesizing Financial Time Series via Alignment of Random Convolutional Attributes

Abstract:

The creation of authentic financial time series presents a significant hurdle, primarily because available training datasets are frequently restricted to a solitary historical trajectory. This paucity of data makes overfitting nearly unavoidable, a problem that is exacerbated during adversarial training when the discriminator risks memorizing the specific training samples. To address this vulnerability, contemporary methods attempt to train generators by minimizing the divergence between untrained feature representations of both real and synthetic time series. However, these previous efforts relied on path signatures, a technique that often fails to capture essential time series characteristics at computationally feasible truncation depths.

In this study, we propose an alternative strategy: training generators by aligning the random convolutional features of real and generated data. While established random convolutional feature maps, such as Rocket and Hydra, have proven effective at providing insightful representations of actual time series, their non-differentiable nature prevents them from supervising generative models. To overcome this limitation, we introduce SOCK (SOft Competing Kernels), a fully differentiable random convolutional feature map specifically designed to train generative time series models. Our experiments demonstrate that generators optimized by matching random SOCK features consistently surpass signature-based and diffusion baselines across a diverse array of financial datasets characterized by small sample sizes. Furthermore, we validate the expressive power of SOCK through two-sample hypothesis testing and time series classification tasks, showing that it either matches or exceeds the performance of existing unsupervised feature maps.

Source: arXiv Generated at: 2026-06-04 00:00:00 UTC