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This work considers a generalization of the INAR(1) model to the panel data first order Seemingly Unrelated INteger AutoRegressive Poisson model, SUINAR(1). It presents Bayesian and classical methodologies to estimate the parameters of Poisson SUINAR(1) model and to forecast future observations of the process. In particular, prediction intervals for forecasts — classical approach — and HPD prediction intervals — Bayesian approach — are derived. A simulation study is provided to give additional insight into the finite sample behaviour of the parameter estimates and forecasts.