Asymptotic behavior of unstable INAR() processes

In this paper the asymptotic behavior of an unstable integer-valued autoregressive model of order p (INAR( p )) is described. Under a natural assumption it is proved that the sequence of appropriately scaled random step functions formed from an unstable INAR( p ) process converges weakly towards a squared Bessel process. We note that this limit behavior is quite different from that of familiar unstable autoregressive processes of order p . An application for Boston armed robberies data set is presented.