Bayesian tensor factorisations for time series of counts

We propose a flexible nonparametric Bayesian modelling framework for multivariate time series of count data based on tensor factorisations. Our models can be viewed as infinite state space Markov chains of known maximal order with non-linear serial dependence through the introduction of appropriate latent variables. Alternatively, our models can be viewed as Bayesian hierarchical models with conditionally independent Poisson distributed observations. Inference about the important lags and their complex interactions is achieved via MCMC. When the observed counts are large, we deal with the resulting computational complexity of Bayesian inference via a two-step inferential strategy based on an initial analysis of a training set of the data. Our methodology is illustrated using simulation experiments and analysis of real-world data.