A real-time method is proposed to obtain a single, consistent probabilistic model to predict future joint angles, velocities, accelerations and jerks, together with the timing for the initial contact, foot flat, heel off and toe off events. In a training phase, a probabilistic principal component model is learned from normal walking, which is used in the online phase for state estimation and prediction. This is validated for normal walking and walking with an exoskeleton. Without exoskeleton, both joint trajectories and gait events are predicted without bias. With exoskeleton, the trajectory prediction is unbiased, but event prediction is slightly biased with a maximum of 33 ms for the toe off event. Performance is compared with predictions based on only the population mean. Without exoskeleton, estimation errors are 5 to 30% lower with our method. With exoskeleton, trajectory prediction errors are up to 20% lower, but gait event prediction errors only improve for foot flat (30%) and are worse for other events (30%-50%). The ability to predict future joint trajectories and gait events offers opportunities to design exoskeleton controllers which anticipate these trajectories and events, allowing better tracking control and smoother, accurately timed transitions between different control modes.