When required to predict sequential events, such as random coin tosses or basketball free throws, people reliably use inappropriate strategies, such as inferring temporal structure when none is present. We investigate the ability of observers to predict sequential events in dynamically changing environments, where there is an opportunity to detect true temporal structure. In two experiments we demonstrate that participants often make correct statistical decisions when asked to infer the hidden state of the data generating process. However, when asked to make predictions about future outcomes, accuracy decreased even though normatively correct responses in the two tasks were identical. A particle filter model accounts for all data, describing performance in terms of a plausible psychological process. By varying the number of particles, and the prior belief about the probability of a change occurring in the data generating process, we were able to model most of the observed individual differences.