A Bivariate Poisson Time Series of Counts with Two Latent Autoregressive Processes

In this paper, we propose a Bivariate Poisson model with two different latent processes to analyze a bivariate time series of counts. The latent processes are introduced to accommodate the temporal correlations while the bivariate model incorporates the cross-correlations between the two time series. The maximum likelihood estimates of the model parameters are obtained by using data cloning approach. A simulation study is carried out to examine the performance of the estimators and the model is applied to a real data set on the asthma-related number of visits to Emergency Departments at hospitals across the Province of Ontario, Canada.