Many common data analysis and machine learning algorithms for time series, such as classification, clustering, or dimensionality reduction, require a distance measurement between pairs of time series in order to determine their similarity. A variety of measures can be found in the literature, each with their own strengths and weaknesses, but the Dynamic Time Warping (DTW) distance measure has occupied an important place since its early applications for the analysis and recognition of spoken word. The main disadvantage of the DTW algorithm is, however, its quadratic time and space complexity, which limits its practical use to relatively small time series. This issue is even more problematic when dealing with streaming time series that are continuously updated, since the analysis must be re-executed regularly and with strict running time constraints. In this paper, we describe enhancements to the DTW algorithm that allow it to be used efficiently in a streaming scenario by supporting an append operation for new time steps with a linear complexity when an exact, error-free DTW is needed, and even better performance when either a Sakoe-Chiba band is used, or when a sliding window is the desired range for the data. Our experiments with one synthetic and four natural data sets have shown that it outperforms other DTW implementations and the potential errors are, in general, much lower than another state-of-the-art approximated DTW technique.