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Data series are a special type of multidimensional data present in numerous domains, where similarity search is a key operation that has been extensively studied in the data series literature. In parallel, the multidimensional community has studied approximate similarity search techniques. We propose a taxonomy of similarity search techniques that reconciles the terminology used in these two domains, we describe modifications to data series indexing techniques enabling them to answer approximate similarity queries with quality guarantees, and we conduct a thorough experimental evaluation to compare approximate similarity search techniques under a unified framework, on synthetic and real datasets in memory and on disk. Although data series differ from generic multidimensional vectors (series usually exhibit correlation between neighboring values), our results show that data series techniques answer approximate %similarity queries with strong guarantees and an excellent empirical performance, on data series and vectors alike. These techniques outperform the state-of-the-art approximate techniques for vectors when operating on disk, and remain competitive in memory.