An abundant literature reports on ‘sequential effects’ observed when humans make predictions on the basis of stochastic sequences of stimuli. Such sequential effects represent departures from an optimal, Bayesian process. A prominent explanation posits that humans are adapted to changing environments, and erroneously assume non-stationarity of the environment, even if the latter is static. As a result, their predictions fluctuate over time. We propose a different explanation in which sub-optimal and fluctuating predictions result from cognitive constraints (or costs), under which humans however behave rationally. We devise a framework of costly inference, in which we develop two classes of models that differ by the nature of the constraints at play: in one case the precision of beliefs comes at a cost, while in the other beliefs with high predictive power are favored. To compare model predictions to human behavior, we carry out a prediction task that uses binary random stimuli, with probabilities ranging from .05 to .95. Although in this task the environment is static and the Bayesian belief converges, subjects’ predictions fluctuate and are biased toward the recent stimulus history. Both classes of models capture this ‘attractive effect’, but they depart in their characterization of higher-order effects. Only the precision-cost model reproduces a ‘repulsive effect’, observed in the data, in which predictions are biased away from stimuli presented in the more distant past. Our experimental results reveal systematic modulations in sequential effects, which our theoretical approach accounts for in terms of rationality under cognitive constraints.