Time series data are increasing at a dramatic rate, yet their analysis remains highly relevant in a wide range of human activities. Due to their volume, existing systems dealing with time series data cannot guarantee interactive response times, even for fundamental tasks such as similarity search. Therefore , in this paper, we present our vision to develop analytic approaches that support exploration and decision making by providing progressive results, before the final and exact ones have been computed. We demonstrate through experiments that providing first approximate and then progressive answers is useful (and necessary) for similarity search queries on very large time series data. Our findings indicate that there is a gap between the time the most similar answer is found and the time when the search algorithm terminates, resulting in inflated waiting times without any improvement. We present preliminary ideas on computing probabilistic estimates of the final results that could help users decide when to stop the search process, i.e., deciding when improvement in the final answer is unlikely, thus eliminating waiting time. Finally, we discuss two additional challenges: how to compute efficiently these probabilistic estimates, and how to communicate them to users.