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Recent work has proposed Wasserstein k-means (Wk-means) clustering as apowerful method to identify regimes in time series data, and one-dimensionalasset returns in particular. In this paper, we begin by studying in detail thebehaviour of the Wasserstein k-means clustering algorithm applied to syntheticone-dimensional time series data. We study the dynamics of the algorithm andinvestigate how varying different hyperparameters impacts the performance ofthe clustering algorithm for different random initialisations. We computesimple metrics that we find are useful in identifying high-quality clusterings.Then, we extend the technique of Wasserstein k-means clustering tomultidimensional time series data by approximating the multidimensionalWasserstein distance as a sliced Wasserstein distance, resulting in a method wecall `sliced Wasserstein k-means (sWk-means) clustering'. We apply thesWk-means clustering method to the problem of automated regime detection inmultidimensional time series data, using synthetic data to demonstrate thevalidity of the approach. Finally, we show that the sWk-means method iseffective in identifying distinct market regimes in real multidimensionalfinancial time series, using publicly available foreign exchange spot rate dataas a case study. We conclude with remarks about some limitations of ourapproach and potential complementary or alternative approaches.

Automated regime detection in multidimensional time series data using sliced Wasserstein k-means clustering