Scan pattern analysis has been discussed as a promising tool in the context of real-time gaze-based applications. In particular, information-theoretic measures of scan path predictability, such as the gaze transition entropy (GTE), have been proposed for detecting relevant changes in user state or task demand. These measures model scan patterns as first-order Markov chains, assuming that only the location of the previous fixation is predictive of the next fixation in time. However, this assumption may not be sufficient in general, as recent research has shown that scan patterns may also exhibit more long-range temporal correlations. Thus, we here evaluate the active information storage (AIS) as a novel information-theoretic approach to quantifying scan path predictability in a dynamic task. In contrast to the GTE, the AIS provides means to statistically test and account for temporal correlations in scan path data beyond the previous last fixation. We compare AIS to GTE in a driving simulator experiment, in which participants drove in a highway scenario, where trials were defined based on an experimental manipulation that encouraged the driver to start an overtaking maneuver. Two levels of difficulty were realized by varying the time left to complete the task. We found that individual observers indeed showed temporal correlations beyond a single past fixation and that the length of the correlation varied between observers. No effect of task difficulty was observed on scan path predictability for either AIS or GTE, but we found a significant increase in predictability during overtaking. Importantly, for participants for which the first-order Markov chain assumption did not hold, this was only shown using AIS but not GTE. We conclude that accounting for longer time horizons in scan paths in a personalized fashion is beneficial for interpreting gaze pattern in dynamic tasks.