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Several methods have been proposed for detecting zero modification in the first-order integer-valued autoregressive (INAR(1)) process. A basic problem of these tests is that they rely upon asymptotic results. In this paper, an alternative test is introduced which makes direct use of the approximate distribution of the number of zeros, which can be described by a beta-binomial distribution. A hybrid estimator of the mean parameter of the marginal distribution of the Poisson INAR(1) process is given. A simulation study shows that power and size of the proposed test are competitive. Finally, real data examples are provided.

An alternative test for zero modification in the INAR(1) model with Poisson innovations