The increased availability of unprecedented amounts of sequential data (generated by Internet-of-Things, as well as scientific applications) has led in the past few years to a renewed interest and attention to the field of data series processing and analysis. Data series collections are processed and analyzed using a large variety of techniques, most of which are based on the computation of some distance function. In this study, we revisit this basic operation of data series distance calculation. We observe that the popular distance measures are oblivious to the correlations inherent in neighboring values in a data series. Therefore, we evaluate the plausibility and benefit of incorporating into the distance function measures of correlation, which enable us to capture the associations among neighboring values in the sequence. We propose four such measures, inspired by statistical and probabilistic approaches, which can effectively model these correlations. We analytically and experimentally demonstrate the benefits of the new measures using the 1NN classification task, and discuss the lessons learned. Finally, we propose future research directions for enabling the proposed measures to be used in practice.