When attempting to predict future events, people commonly rely on historical data. One psychological characteristic of judgmental forecasting of time series, established by research, is that when people make forecasts from series they tend tounderestimate future values for upward trends and overestimate them for downward ones, so-called ‘trend-damping’ (modeled by anchoring on, and insufficient adjustment from, the average of recent time series values). Events in a time series can beexperienced sequentially (dynamic mode) or they can also be retrospectively viewed simultaneously (static mode), not experienced individually in real time. In one experiment, we studied the influence of presentation mode (dynamic and static) ontwo sorts of judgment: (i) predictions of the next event (forecast), and (ii) estimation of the average value of all the events in the presented series (average estimation). Participants’ responses in dynamic mode were anchored on more recent events thanin static mode for all types of judgment but with different consequences; hencedynamic presentation improved prediction accuracy, but not estimation. These results are not anticipated by existing theoretical accounts; we develop and present an agent based model - the Adaptive Anchoring Model (ADAM) to account for the difference between processing sequences of dynamically and statically presented stimuli( visually presented data). ADAM captures how variation in presentation modeproduces variation in responses (and the accuracy of these responses) in both forecasting and judgment tasks. ADAM’s model predictions for the forecasting and judgment tasks fit better with the response data than a linear-regression time series model. Moreover, ADAM outperformed autoregressive-integrated-moving-average (ARIMA) and exponential-smoothing models, while neither of these models accountsfor people’s responses on the average estimation task.