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

Abstract

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.

Bayesian modeling of multivariate time series of counts

“…The proposed approach enabled the authors to directly sample from the posterior distributions of the parameters. In a more recent paper, Al‐Wahsh and Hussein (2020) presented Bayesian analysis of the bivariate Poisson state space model to analyze daily time series of Asthma‐related ER visits.…”

“…The proposed approach enabled the authors to directly sample from the posterior distributions of the parameters. In a more recent paper, Al-Wahsh and Hussein (2020) Vector time series Y it is assumed to follow a J dimensional MVP distribution with parameter vector λ it denoted as…”