The problem of rapid and automated detection of distinct market regimes is a topic of great interest to financial mathematicians and practitioners alike. In this paper, we outline an unsupervised learning algorithm for clustering financial time-series into a suitable number of temporal segments (market regimes). As a special case of the above, we develop a robust algorithm that automates the process of classifying market regimes. The method is robust in the sense that it does not depend on modelling assumptions of the underlying time series as our experiments with real datasets show. This method -- dubbed the Wasserstein $k$-means algorithm -- frames such a problem as one on the space of probability measures with finite $p^\text{th}$ moment, in terms of the $p$-Wasserstein distance between (empirical) distributions. We compare our WK-means approach with a more traditional clustering algorithms by studying the so-called maximum mean discrepancy scores between, and within clusters. In both cases it is shown that the WK-means algorithm vastly outperforms all considered competitor approaches. We demonstrate the performance of all approaches both in a controlled environment on synthetic data, and on real data.
翻译:快速和自动发现不同市场制度的问题是金融数学家和从业者都非常感兴趣的一个专题。在本文中,我们概述了将金融时间序列组合成适当数量的时段(市场制度)的不受监督的学习算法。作为上述一个特例,我们开发了一种强大的算法,使市场制度分类过程自动化。这个方法很健全,因为它并不象我们用真实数据集进行的实验所显示的那样,取决于对基本时间序列的模型假设。这种方法 -- -- 称为瓦西斯坦 $k$-poors 运算法 -- -- 将问题标为用有限 $p{text{th} 时间段计量概率空间的问题,以美元/Wasserstein在(精神上)分布之间的距离为单位。我们通过研究所谓的最大平均差分数和组内的数据,将我们的WK手段方法与较传统的组算法进行比较。在这两种情况下,WK手段都显示WK手段大大超越了所有据认为的兼容性方法。我们展示了在受控的合成数据环境中和数据环境中的所有方法的性。