  This paper introduces multivariate Poisson autoregressive models with
exogenous covariates (PoARX) for modelling multivariate time series of counts.
We obtain conditions for the 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 obtaining 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 suggesting some further areas of application and by listing directions for
future work.
