PoARX models for count time series

This paper introduces multivariate Poisson autoregressive models with exogenous covariates (PoARX) for modelling multivariate time series of counts. We state conditions for a PoARX process to be stationary and ergodic before proposing a computationally efficient procedure for estimation of parameters by the method of inference functions (IFM) and stating asymptotic normality of these estimators. Lastly, we demonstrate an application to count data for the number of people entering and exiting a building, and show how the different aspects of the model combine to produce a strong predictive model. We conclude by listing directions for future work.