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This paper presents and analyzes an incremental system for clustering streaming time series. The Online Divisive-Agglomerative Clustering (ODAC) system continuously maintains a tree-like hierarchy of clusters that evolves with data, using a top-down strategy. The splitting criterion is a correlation-based dissimilarity measure among time series, splitting each node by the farthest pair of streams. The system also uses a merge operator that reaggregates a previously split node in order to react to changes in the correlation structure between time series. The split and merge operators are triggered in response to changes in the diameters of existing clusters, assuming that in stationary environments, expanding the structure leads to a decrease in the diameters of the clusters. The system is designed to process thousands of data streams that flow at a high rate. The main features of the system include update time and memory consumption that do not depend on the number of examples in the stream. Moreover, the time and memory required to process an example decreases whenever the cluster structure expands. Experimental results on artificial and real data assess the processing qualities of the system, suggesting a competitive performance on clustering streaming time series, exploring also its ability to deal with concept drift.