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Three robust methods for clustering multivariate time series from the pointof view of generating processes are proposed. The procedures are robustversions of a fuzzy C-means model based on: (i) estimates of the quantilecross-spectral density and (ii) the classical principal component analysis.Robustness to the presence of outliers is achieved by using the so-calledmetric, noise and trimmed approaches. The metric approach incorporates in theobjective function a distance measure aimed at neutralizing the effect of theoutliers, the noise approach builds an artificial cluster expected to containthe outlying series and the trimmed approach eliminates the most atypicalseries in the dataset. All the proposed techniques inherit the nice propertiesof the quantile cross-spectral density, as being able to uncover general typesof dependence. Results from a broad simulation study including multivariatelinear, nonlinear and GARCH processes indicate that the algorithms aresubstantially effective in coping with the presence of outlying series (i.e.,series exhibiting a dependence structure different from that of the majority),clearly poutperforming alternative procedures. The usefulness of the suggestedmethods is highlighted by means of two specific applications regardingfinancial and environmental series.

Quantile-based fuzzy C-means clustering of multivariate time series: Robust techniques