Asymptotic behavior of unstable INAR(p) processes

Details Asymptotic behavior of unstable INAR(p) processes Asymptotic behavior of unstable INAR(p) processes

2009-08-31

arxiv.org/abs/0908.4560v5

Stochastic Processes and their Applications 121(3), 2011, 583-608

Mathematics

Probability

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

Scientific paper

10.1016/j.spa.2010.11.005

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.

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