Autoregressive metric-based trimmed fuzzy clustering with an application to PM10 time series

- A fuzzy clustering model for time series of air pollutant is proposed.
- Clustering relies on the autoregressive representation of the time series.
- The clustering model is robust to the presence of outlier time series.
- The robustness is achieved by means of the impartial trimmed approach.

Air quality measurement relies on the effectiveness of a network of monitoring stations. Monitoring stations collect information about the evolution of air pollutants concentration. If more stations supplies the same information, then some of them could be deemed as redundant. Then, a clustering model for time series is useful to identify stations with similar features. Time series of pollutant concentration can be classified using the autoregressive metric in the framework of standard clustering techniques. A serious drawback is related to the lack of robustness of standard procedures. In this paper, using a partitioning around medoids approach combined with a trimming-based rule, a fuzzy model for cluster time series is proposed. The model provides a robust alternative to standard procedures. Two simulation studies are carried out to evaluate the clustering performance of the proposed clustering model. Finally, an empirical application to real time series of PM10 concentration in the Lazio region is presented and discussed showing the practical usefulness of the proposed approach.