In this work we present a non-parametric online market regime detection method for multidimensional data structures using a path-wise two-sample test derived from a maximum mean discrepancy-based similarity metric on path space that uses rough path signatures as a feature map. The latter similarity metric has been developed and applied as a discriminator in recent generative models for small data environments, and has been optimised here to the setting where the size of new incoming data is particularly small, for faster reactivity. On the same principles, we also present a path-wise method for regime clustering which extends our previous work. The presented regime clustering techniques were designed as ex-ante market analysis tools that can identify periods of approximatively similar market activity, but the new results also apply to path-wise, high dimensional-, and to non-Markovian settings as well as to data structures that exhibit autocorrelation. We demonstrate our clustering tools on easily verifiable synthetic datasets of increasing complexity, and also show how the outlined regime detection techniques can be used as fast on-line automatic regime change detectors or as outlier detection tools, including a fully automated pipeline. Finally, we apply the fine-tuned algorithms to real-world historical data including high-dimensional baskets of equities and the recent price evolution of crypto assets, and we show that our methodology swiftly and accurately indicated historical periods of market turmoil.

翻译：本文提出了一种针对多维数据结构的非参数在线市场状态检测方法，该方法利用路径空间上基于最大平均差异的相似性度量，以粗糙路径签名作为特征映射，推导出路径化双样本检验。该相似性度量已在近期小数据环境下的生成模型中作为判别器得到开发与应用，且在此针对新到达数据量极小的场景进行了优化，以实现更快速的响应。基于相同原理，我们还提出了一种路径化的状态聚类方法，作为先前工作的拓展。所提出的状态聚类技术被设计为事前市场分析工具，能够识别近似相似的市场活动时期，但新的结果同样适用于路径化、高维度、非马尔可夫场景以及呈现自相关性的数据结构。我们在复杂度递增且易于验证的合成数据集上展示了聚类工具的性能，并说明如何将所述状态检测技术用作快速在线自动状态变化检测器或异常值检测工具（包括完全自动化流程）。最后，我们将微调后的算法应用于真实世界的历史数据（包括高维股票篮子及近期加密货币资产价格演变），结果表明我们的方法能够迅速且准确地指示出历史市场动荡时期。