Clustering Market Regimes using the Wasserstein Distance

TL;DR

This paper introduces a Wasserstein k-means clustering algorithm for automatically identifying and classifying market regimes in financial time-series data, outperforming traditional methods in robustness and accuracy.

Contribution

The paper develops a novel Wasserstein k-means algorithm for market regime detection that does not rely on model assumptions and demonstrates superior performance over existing methods.

Findings

Wasserstein k-means outperforms traditional clustering algorithms.

The method is robust and model-free.

Effective on both synthetic and real datasets.

Abstract

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.