A bivariate autoregressive Poisson model and its application to asthma-related emergency room visits

There are no gold standard methods that perform well in every situation when it comes to the analysis of multiple time series of counts. In this paper, we consider a positively correlated bivariate time series of counts and propose a parameter-driven Poisson regression model for its analysis. In our proposed model, we employ a latent autoregressive process, AR(p) to accommodate the temporal correlations in the two series. We compute the familiar maximum likelihood estimators of the model parameters and their standard errors via a Bayesian data cloning approach. We apply the model to the analysis of a bivariate time series arising from asthma-related visits to emergency rooms across the Canadian province of Ontario.