Asymptotic behavior of unstable INAR(p) processes

Abstract

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.

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

References in corpus (2)

• The asymptotic structure of nearly unstable non-negative integer-valued AR(1) models
• p-order rounded integer-valued autoregressive (RINAR(p)) process

Cited by in corpus (7)

• Limit theorems for nearly unstable Hawkes processes
• Asymptotic behavior of CLS estimator of autoregressive parameter for nonprimitive unstable INAR(2) models
• Asymptotic behavior of CLS estimators for $2$-type doubly symmetric critical Galton-Watson processes with immigration
• Asymptotic behavior of CLS estimators for unstable INAR(2) models
• Statistical inference for critical continuous state and continuous time branching processes with immigration
• On aggregation of multitype Galton-Watson branching processes with immigration
• Asymptotic behavior of critical primitive multi-type branching processes with immigration