  Time series clustering is an essential machine learning task with
applications in many disciplines. While the majority of the methods focus on
time series taking values on the real line, very few works consider time series
defined on the unit circle, although the latter objects frequently arise in
many applications. In this paper, the problem of clustering circular time
series is addressed. To this aim, a distance between circular series is
introduced and used to construct a clustering procedure. The metric relies on a
new measure of serial dependence considering circular arcs, thus taking
advantage of the directional character inherent to the series range. Since the
dynamics of the series may vary over the time, we adopt a fuzzy approach, which
enables the procedure to locate each series into several clusters with
different membership degrees. The resulting clustering algorithm is able to
group series generated from similar stochastic processes, reaching accurate
results with series coming from a broad variety of models. An extensive
simulation study shows that the proposed method outperforms several alternative
techniques, besides being computationally efficient. Two interesting
applications involving time series of wind direction in Saudi Arabia highlight
the potential of the proposed approach.
