Brain activity during wakeful rest, where no instructions are provided by the experimenter except for keeping it quiet, can offer important insights about unconstrained cognition. In particular, it has been shown to be significantly predictive of various subject psychological and/or clinical traits. Typically, we make out-of-sample predictions of the individual traits by constructing features from the data that are based on averages across the entire experimental session, which are then fed to a machine learning method. While just looking at session-averages is a crude simplification of the workings of the brain, it is far from obvious how to construct features that take into account the dynamics of brain activity given that, in an unconstrained cognition paradigm, we cannot align the subjects' data temporally. In this talk, I will describe a novel approach where we combine Hidden Markov modelling with a kernel-based prediction method to make predictions of subject traits (such as intelligence) using information of how people's brain activity fluctuates.