Dynamic staged trees for discrete multivariate time series: forecasting, model selection and causal analysis

A new tree-based graphical model --- the dynamic staged tree --- is proposed for modelling discrete-valued discrete-time multivariate processes which are hypothesised to exhibit symmetries in how some intermediate situations might unfold. We define and implement a one-step-ahead prediction algorithm with the model using multi-process modelling and the power steady model that is robust to short-term variations in the data yet sensitive to underlying system changes. We demonstrate that the whole analysis can be performed in a conjugate way so that the potentially vast model space can be traversed quickly and then results communicated transparently. We also demonstrate how to analyse a general set of causal hypotheses on this model class. Our techniques are illustrated using a simple educational example.