  Recent work has proposed Wasserstein k-means (Wk-means) clustering as a
powerful method to identify regimes in time series data, and one-dimensional
asset returns in particular. In this paper, we begin by studying in detail the
behaviour of the Wasserstein k-means clustering algorithm applied to synthetic
one-dimensional time series data. We study the dynamics of the algorithm and
investigate how varying different hyperparameters impacts the performance of
the clustering algorithm for different random initialisations. We compute
simple metrics that we find are useful in identifying high-quality clusterings.
Then, we extend the technique of Wasserstein k-means clustering to
multidimensional time series data by approximating the multidimensional
Wasserstein distance as a sliced Wasserstein distance, resulting in a method we
call `sliced Wasserstein k-means (sWk-means) clustering'. We apply the
sWk-means clustering method to the problem of automated regime detection in
multidimensional time series data, using synthetic data to demonstrate the
validity of the approach. Finally, we show that the sWk-means method is
effective in identifying distinct market regimes in real multidimensional
financial time series, using publicly available foreign exchange spot rate data
as a case study. We conclude with remarks about some limitations of our
approach and potential complementary or alternative approaches.
