In this paper we study the interval scoring rule as a mechanism to elicit subjective beliefs under varying degrees of uncertainty. In our experiment, subjects forecast the termination time of a time series to be generated from a given but unknown stochastic process. Subjects gradually learn more about the underlying process over time and hence the true distribution over termination times. We conduct two treatments, one with a high and one with a low volatility process. We find that elicited intervals are better when subjects are facing a low volatility process. In this treatment, participants learn to position their intervals almost optimally over the course of the experiment. This is in contrast with the high volatility treatment, where subjects, over the course of the experiment, learn to optimize the location of their intervals but fail to provide the optimal length.