Fuzzy Clustering of Circular Time Series With Applications to Wind Data

In environmental science, practitioners often deal with data recorded sequentially along time, such as time series of wind direction or wind speed. In this context, clustering of time series is a useful tool to carry out exploratory analyses. While most of the proposals are focused on real-valued time series, very few works consider circular time series, despite the frequent appearance of these objects in many disciplines. In this manuscript, a dissimilarity for circular time series is introduced and used in combination with a soft clustering method. The metric relies on a measure of serial dependence considering circular arcs, thus taking advantage of the directional character inherent to the series range. The clustering approach is able to group together time series generated from similar stochastic processes. Some simulations show that the method exhibits a reasonable clustering effectiveness, outperforming alternative techniques in many contexts. Two interesting applications involving time series of wind direction in Saudi Arabia show the potential of the proposed approach.