Abstract. We discuss the problem of deriving an estimative prediction limit as well as a simulation-based improved prediction limit for a future realization from the stationary, first-order Poisson INAR(1) process. An assessment of these limits was carried out by calculating their coverage probability, conditional on the last observation. It was found that while an estimative prediction limit may always be calculated, an improved prediction limit may not be obtained due to its discreteness and expectation to obtain a coherent prediction.