In this paper the asymptotic behavior of the conditional least squares estimators of the autoregressive parameters $(α,β)$, of the stability parameter $\varrho := α+ β$, and of the mean $μ$ of the innovation $\vare_k$, $k \in \NN$, for an unstable integer-valued autoregressive process $X_k = α\circ X_{k-1} + β\circ X_{k-2} + \vare_k$, $k \in \NN$, is described. The limit distributions and the scaling factors are different according to the following three cases: (i) decomposable, (ii) indecomposable but not positively regular, and (iii) positively regular models.