Generating Financial Time Series by Matching Random Convolutional Features

2026-06-03

AI Summary

This work addresses the challenge of overfitting in generative modeling of financial time series under extremely limited data settings—specifically, when only a single historical path is available. To overcome the instability and overfitting commonly induced by adversarial training in such few-shot scenarios, the authors propose SOCK (SOft Competing Kernels), a fully differentiable stochastic convolutional feature mapping. Generator training is supervised by aligning these features between real and synthetic sequences, entirely eliminating the need for a learnable discriminator. This approach represents the first effective application of random convolutional features to time series generation. Empirical results demonstrate that SOCK significantly outperforms baseline methods based on path signatures and diffusion models across multiple financial datasets, while also achieving superior performance in statistical hypothesis testing and downstream classification tasks.

Abstract

Generating realistic financial time series is challenging as training data is often limited to a single historical path. With such scarce data, overfitting is hard to avoid, especially under adversarial training where a trained discriminator can memorize the training samples. To mitigate this, recent approaches train generators to minimize the discrepancy between untrained feature representations of real and generated time series. In these works, the feature maps are based on path signatures, which can fail to capture relevant time series properties at tractable truncation depths. In this work, we instead train generators by matching random convolutional features of real and generated time series. Existing random convolutional feature maps, such as Rocket and Hydra, have been shown to provide informative representations of real-world time series, but cannot supervise generative models because they are non-differentiable. We introduce SOCK (SOft Competing Kernels), a fully differentiable random convolutional feature map, suited to train generative time series models. We show that generators trained by matching random SOCK features consistently outperform signature and diffusion baselines across a wide range of small-sample financial datasets. We further demonstrate SOCK's expressiveness on two-sample hypothesis testing and time series classification tasks, where SOCK matches or outperforms existing unsupervised feature maps.

Problem

• financial time series generation
• data scarcity
• overfitting
• feature representation
• time series modeling

Innovation

• SOCK
• random convolutional features
• differentiable feature maps
• financial time series generation
• small-sample learning