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Time series clustering is a central machine learning task with applicationsin many fields. While the majority of the methods focus on real-valued timeseries, very few works consider series with discrete response. In this paper,the problem of clustering ordinal time series is addressed. To this aim, twonovel distances between ordinal time series are introduced and used toconstruct fuzzy clustering procedures. Both metrics are functions of theestimated cumulative probabilities, thus automatically taking advantage of theordering inherent to the series' range. The resulting clustering algorithms arecomputationally efficient and able to group series generated from similarstochastic processes, reaching accurate results even though the series comefrom a wide variety of models. Since the dynamic of the series may vary overthe time, we adopt a fuzzy approach, thus enabling the procedures to locateeach series into several clusters with different membership degrees. Anextensive simulation study shows that the proposed methods outperform severalalternative procedures. Weighted versions of the clustering algorithms are alsopresented and their advantages with respect to the original methods arediscussed. Two specific applications involving economic time series illustratethe usefulness of the proposed approaches.

Fuzzy clustering of ordinal time series based on two novel distances with economic applications