Fuzzy clustering of ordinal time series based on two novel distances with economic applications
This addresses a gap in time series clustering for ordinal data, with applications in economics, but is incremental as it builds on existing fuzzy clustering with new distances.
The paper tackles the problem of clustering ordinal time series, which have discrete responses, by introducing two novel distances based on estimated cumulative probabilities and using them in fuzzy clustering procedures, resulting in methods that outperform alternatives in simulations and are applied to economic data.
Time series clustering is a central machine learning task with applications in many fields. While the majority of the methods focus on real-valued time series, very few works consider series with discrete response. In this paper, the problem of clustering ordinal time series is addressed. To this aim, two novel distances between ordinal time series are introduced and used to construct fuzzy clustering procedures. Both metrics are functions of the estimated cumulative probabilities, thus automatically taking advantage of the ordering inherent to the series' range. The resulting clustering algorithms are computationally efficient and able to group series generated from similar stochastic processes, reaching accurate results even though the series come from a wide variety of models. Since the dynamic of the series may vary over the time, we adopt a fuzzy approach, thus enabling the procedures to locate each series into several clusters with different membership degrees. An extensive simulation study shows that the proposed methods outperform several alternative procedures. Weighted versions of the clustering algorithms are also presented and their advantages with respect to the original methods are discussed. Two specific applications involving economic time series illustrate the usefulness of the proposed approaches.