Robust fuzzy clustering based on quantile autocovariances

Robustness to the presence of outliers in time series clustering is addressed. Assuming that the clustering principle is to group realizations of series generated from similar dependence structures, three robust versions of a fuzzy C-medoids model based on comparing sample quantile autocovariances are proposed by considering, respectively, the so-called metric, noise, and trimmed approaches. Each method achieves its robustness against outliers in different manner. The metric approach considers a suitable transformation of the distance aimed at smoothing the effect of the outliers, the noise approach brings together the outliers into a separated artificial cluster, and the trimmed approach removes a fraction of the time series. All the proposed approaches take advantage of the high capability of the quantile autocovariances to discriminate between independent realizations from a broad range of stationary processes, including linear, non-linear and conditional heteroskedastic models. An extensive simulation study involving scenarios with different generating models and contaminated with outliers is performed. Robustness against (i) outliers generated from different generating patterns, and (ii) outliers characterized by isolated, temporary or persistent level changes is evaluated. The influence of the input parameters required by the different algorithms is analyzed. Regardless of the considered models, the results show that the proposed robust procedures are able to neutralize the effect of the anomalous series preserving the true clustering structure, and fairly outperform other robust algorithms based on alternative metrics. Two applications to financial data sets permit to illustrate the usefulness of the proposed models.