Robust fuzzy clustering of time series based on B-splines

Four different approaches to robust fuzzy clustering of time series are presented and compared with respect to other existent approaches. These approaches are useful to cluster time series when outlying values are found in these time series, which is often the rule in most real data applications. A representation of the time series by using B-splines is considered and, later, robust fuzzy clustering methods are applied on the B-splines fitted coefficients. Feasible algorithms for implementing these methodologies are presented. A simulation study shows how these methods are useful to deal with contaminating time series and also switching time series due to fuzziness. A real data analysis example on financial data is also presented.