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In finance, cluster analysis is a tool particularly useful for classifying stock market multivariate time series data related to daily returns, volatility daily stocks returns, commodity prices, volume trading, index, enhanced index tracking portfolio, and so on. In the literature, following different methodological approaches, several clustering methods have been proposed for clustering multivariate time series. In this paper by adopting a fuzzy approach and using the Partitioning Around Medoids strategy, we suggest to cluster multivariate financial time series by considering the dynamic time warping distance. In particular, we proposed a robust clustering method capable to neutralize the negative effects of possible outliers in the clustering process. The clustering method achieves its robustness by adopting a suitable trimming procedure to identify multivariate financial time series more distant from the bulk of data. The proposed clustering method is applied to the stocks composing the FTSE MIB index to identify common time patterns and possible outliers. [ABSTRACT FROM AUTHOR]

In this paper we propose different robust fuzzy clustering models for classifying heteroskedastic (volatility) time series, following the so-called model-based approach to time series clustering and using a partitioning around medoids procedure. The proposed models are based on a GARCH parametric modeling of the time series, i.e. the unconditional volatility and the time-varying volatility GARCH representation of the time series. We first suggest a timid robustification of the fuzzy clustering. Then, we propose three robust fuzzy clustering models belonging to the so-called metric, noise and trimmed approaches, respectively. Each model neutralizes the negative effects of the outliers in the clustering process in a different manner. In particular, the first robust model, based on the metric approach, achieves its robustness with respect to outliers by taking into account a “robust” distance measure; the second, based on the noise approach, achieves its robustness by introducing a noise cluster represented by a noise prototype; the third, based on the trimmed approach, achieves its robustness by trimming away a certain fraction of outlying time series. The usefulness and effectiveness of the proposed clustering models is illustrated by means of a simulation study and two applications in finance and economics. [ABSTRACT FROM AUTHOR]

Abstract: Robust fuzzy clustering models for fuzzy data are proposed. In particular, using a “Partitioning Around Medoids” (PAM) approach, first a timid robustification of fuzzy clustering for a general class of fuzzy data is proposed. Successively, we propose three robust fuzzy clustering models based on, respectively, the so-called metric, noise and trimmed approaches. The metric approach achieves its robustness with respect to outliers by taking into account a “robust” distance measure, the noise approach by introducing a noise cluster represented by a noise prototype, and the trimmed approach by trimming away a certain fraction of data units. A comparative simulation study and measures of misclassification and of robustness with respect to prototype detection in the presence of outliers have been developed. Several applications to chemometrical and benchmark data are also presented. [Copyright &y& Elsevier]

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 PM 10 concentration in the Lazio region is presented and discussed showing the practical usefulness of the proposed approach. [ABSTRACT FROM AUTHOR]