Trust between agents in multi-agent systems (MASs) is critical to encourage high levels of cooperation. Existing methods to assess trust and reputation use direct and indirect past experiences about an agent to estimate their future performance; however, these will not always be representative if agents change their behaviour over time. Real-world distributed networks such as online market places, P2P networks, pervasive computing and the Smart Grid can be viewed as MAS. Dynamic agent behaviour in such MAS can arise from seasonal changes, cheaters, supply chain faults, network traffic and many other reasons. However, existing trust and reputation models use limited techniques, such as forgetting factors and sliding windows, to account for dynamic behaviour. In this paper, we propose Reacting and Predicting in Trust and Reputation (RaPTaR), a method to extend existing trust and reputation models to give agents the ability to monitor the output of interactions with a group of agents over time to identify any likely changes in behaviour and adapt accordingly. Additionally, RaPTaR can provide an a priori estimate of trust when there is little or no interaction data (either because an agent is new or because a detected behaviour change suggests recent past experiences are no longer representative). Our results show that RaPTaR has improved performance compared to existing trust and reputation methods when dynamic behaviour causes the ranking of the best agents to interact with to change.