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Asymptotic behavior of unstable INAR(p) processes

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  • Barczy, M.
  • Ispány, M.
  • Pap, G.

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.

Suggested Citation

  • Barczy, M. & Ispány, M. & Pap, G., 2011. "Asymptotic behavior of unstable INAR(p) processes," Stochastic Processes and their Applications, Elsevier, vol. 121(3), pages 583-608, March.
    • Handle: RePEc:eee:spapps:v:121:y:2011:i:3:p:583-608
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    1. Mátyás Barczy & Márton Ispány & Gyula Pap, 2014. "Asymptotic Behavior of Conditional Least Squares Estimators for Unstable Integer-valued Autoregressive Models of Order 2," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 41(4), pages 866-892, December.
    2. Barczy, Mátyás & Körmendi, Kristóf & Pap, Gyula, 2015. "Statistical inference for 2-type doubly symmetric critical irreducible continuous state and continuous time branching processes with immigration," Journal of Multivariate Analysis, Elsevier, vol. 139(C), pages 92-123.
    3. Barczy, Mátyás & Bezdány, Dániel & Pap, Gyula, 2023. "Asymptotic behaviour of critical decomposable 2-type Galton–Watson processes with immigration," Stochastic Processes and their Applications, Elsevier, vol. 160(C), pages 318-350.
    4. Kristóf Körmendi & Gyula Pap, 2018. "Statistical inference of 2-type critical Galton–Watson processes with immigration," Statistical Inference for Stochastic Processes, Springer, vol. 21(1), pages 169-190, April.

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