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.
Keywords: Bayesian estimation; Parameter-driven; bivariate Poisson; data cloning; state-space models; time series of counts.
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