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.Comment: 35 pages; corrected and extended version: a new section on an
application for Boston armed robberies data set is adde
