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Time series data are commonly clustered based on their distributional characteristics. The moments play a central role among such characteristics because of their relevant informative content. This paper aims to develop a novel approach that faces still open issues in moment-based clustering. First of all, we deal with a very general framework of time-varying moments rather than static quantities. Second, we include in the clustering model high-order moments. Third, we avoid implicit equal weighting of the considered moments by developing a clustering procedure that objectively computes the optimal weight for each moment. As a result, following a fuzzy approach, two weighted clustering models based on both unconditional and conditional moments are proposed. Since the Dynamic Conditional Score model is used to estimate both conditional and unconditional moments, the resulting framework is called weighted score-driven clustering. We apply the proposed method to financial time series as an empirical experiment. • The paper proposes a new method for time series clustering. • The procedure is based on an optimal combination of conditional and unconditional moments. • The clustering procedure includes fuzziness. • The clustering method is applied to financial time series. [ABSTRACT FROM AUTHOR]