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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 modelingof 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

In this paper, following a partitioning around medoids approach, a fuzzy\ud clustering model for interval-valued data, i.e., FCMd-ID, is introduced. Successively,\ud for avoiding the disruptive effects of possible outlier interval-valued data in the clustering\ud process, a robust fuzzy clustering model with a trimming rule, called Trimmed\ud Fuzzy C-medoids for interval-valued data (TrFCMd-ID), is proposed. In order to\ud show the good performances of the robust clustering model, a simulation study and\ud two applications are provided

We evaluate the magnitude of the disparities in the demand for redistribution across European countries and American states during the 2000s. Modelling the demand for redistribution in a multilevel framework, we identify the determinants that contribute the most in predicting support for redistribution. We observe that individual characteristics and contextual variables are associated with demand for redistribution in the same way in Europe and in the US, whereas others exert different influences on the probability of supporting redistribution. We find important differences from some well‐established evidence obtained from data collected for the 1980s and the 1990s.