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In this paper the asymptotic behavior of the conditional least squaresestimators of the autoregressive parameters $(\alpha,\beta)$, of the stabilityparameter $\varrho := \alpha + \beta$, and of the mean $\mu$ of the innovation$\vare_k$, $k \in \NN$, for an unstable integer-valued autoregressive process$X_k = \alpha \circ X_{k-1} + \beta \circ X_{k-2} + \vare_k$, $k \in \NN$, isdescribed. The limit distributions and the scaling factors are differentaccording to the following three cases: (i) decomposable, (ii) indecomposablebut not positively regular, and (iii) positively regular models.

Asymptotic behavior of CLS estimators for unstable INAR(2) models