金融时间序列生成终于有了一个可微的随机卷积特征方案，做量化分析或金融建模的团队可以直接用SOCK替代签名特征，小样本场景下效果更好。
金融时间序列生成面临训练数据稀缺（通常只有一条历史路径）的挑战，导致对抗训练容易过拟合。现有方法通过匹配路径签名特征来训练生成器，但签名特征在有限截断深度下无法捕捉关键时间序列属性。本文提出SOCK（软竞争核），一种完全可微的随机卷积特征映射，能够有效监督生成模型。实验表明，基于SOCK特征匹配训练的生成器在多个小样本金融数据集上持续优于签名和扩散基线方法。此外，SOCK在双样本假设检验和时间序列分类任务中也匹配或超越了现有无监督特征映射。
Generating Financial Time Series by Matching Random Convolutional Features
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.