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Clustering Market Regimes using the Wasserstein Distance

Author

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  • Blanka Horvath
  • Zacharia Issa
  • Aitor Muguruza
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.

Suggested Citation

  • Blanka Horvath & Zacharia Issa & Aitor Muguruza, 2021. "Clustering Market Regimes using the Wasserstein Distance," Papers 2110.11848, arXiv.org.
    • Handle: RePEc:arx:papers:2110.11848
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    References listed on IDEAS

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    1. John M. Maheu & Thomas H. McCurdy & Yong Song, 2012. "Components of Bull and Bear Markets: Bull Corrections and Bear Rallies," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 30(3), pages 391-403, February.
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    7. Dias, José G. & Vermunt, Jeroen K. & Ramos, Sofia, 2015. "Clustering financial time series: New insights from an extended hidden Markov model," European Journal of Operational Research, Elsevier, vol. 243(3), pages 852-864.
    8. Hamilton, James D, 1989. "A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle," Econometrica, Econometric Society, vol. 57(2), pages 357-384, March.
    9. Hans Buhler & Blanka Horvath & Terry Lyons & Imanol Perez Arribas & Ben Wood, 2020. "A Data-driven Market Simulator for Small Data Environments," Papers 2006.14498, arXiv.org.
    10. Blanka Horvath & Aitor Muguruza & Mehdi Tomas, 2019. "Deep Learning Volatility," Papers 1901.09647, arXiv.org, revised Aug 2019.
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    Cited by:

    1. Yannick Limmer & Blanka Horvath, 2023. "Robust Hedging GANs," Papers 2307.02310, arXiv.org.
    2. Zacharia Issa & Blanka Horvath, 2023. "Non-parametric online market regime detection and regime clustering for multidimensional and path-dependent data structures," Papers 2306.15835, arXiv.org.

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