Estimation of time depends heavily on both global and local statistical context. Durations that are short relative to the global distribution are systematically overestimated; durations that are locally preceded by long durations are also overestimated. Context effects are prominent in duration discrimination tasks, where a standard duration and a comparison duration are presented on each trial. In this study, we compare and test two models that posit a dynamically updating internal reference that biases time estimation on global and local scales in duration discrimination tasks. The internal reference model suggests that the internal reference operates during postperceptual stages and only interacts with the first presented duration. In contrast, a Bayesian account of time estimation implies that any perceived duration updates the internal reference and therefore interacts with both the first and second presented duration. We implemented both models and tested their predictions in a duration discrimination task where the standard duration varied from trial to trial. Our results are in line with a Bayesian perspective on time estimation. First, the standard systematically biased estimation of the comparison, such that shorter standards increased the likelihood of reporting that the comparison was shorter. Second, both the previous standard and comparison systematically biased time estimation of subsequent trials in the same direction. Third, more precise observers showed smaller biases. In sum, our findings suggest a common dynamic prior for time that is updated by each perceived duration and where the relative weighting of old and new observations is determined by their relative precision.