Clustering complex time-series databases by using periodic components

Clustering methods for time series have been widely studied and applied within a range of different fields. They are generally based on the choice of a relevant metric. The aim of this paper is to propose and discuss a clustering technique in the frequency domain for stationary time series. The idea of the new procedure consists in analyzing the discrete component of the spectrum, avoiding the introduction of any metric for the classification of the time series. The novel technique is suitable for time series that show strong periodic components and is based on an efficient algorithm requiring less computational and memory resources, making it appropriate for large and complex temporal databases. The problem of the selection of the optimal partition is also addressed along with a proposal that takes into account the stability of the clusters and the efficiency of the procedure in classifying the time series among the different groups. The results of a simulation study show the relative merits of the proposed procedure compared to other spectral-based approaches. An application to a large time-series database provided by a big electric company is also discussed. The application showed the good performance of the proposed technique, which was able to classify the time series in a few groups of customers with homogeneous electricity demand patterns.