Abstract
Integer-valued autoregressive processes of a general order p≥1 (INAR(p) processes) are considered, and the focus is put on the time-reversibility of these processes. It is shown that for the case p=1 the time-reversibility of such a process already implies that the innovations are Poisson distributed. For the case of a general p≥2, two competing formulations for the INAR(p) process of Alzaid and Al-Osh (in J. Appl. Prob. 27(2):314–324, 1990) and Du and Li (in J. Time Ser. Anal. 12(2):129–142, 1991) are considered. While the INAR(p) process as defined by Alzaid and Al-Osh behaves analogously to the INAR(1) process, the INAR(p) process of Du and Li is shown to be time-irreversible in general.
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Acknowledgements
The author is grateful to Prof. Christian Weiß for carefully reading the paper and for helpful suggestions which greatly improved the paper.
The author’s research has been supported by the Deutsche Forschungsgemeinschaft (German Research Foundation) within the programme “Statistical Modeling of Complex Systems and Processes – Advanced Nonparametric Approaches”, grant GRK 1953.
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Schweer, S. (2015). On the Time-Reversibility of Integer-Valued Autoregressive Processes of General Order. In: Steland, A., Rafajłowicz, E., Szajowski, K. (eds) Stochastic Models, Statistics and Their Applications. Springer Proceedings in Mathematics & Statistics, vol 122. Springer, Cham. https://doi.org/10.1007/978-3-319-13881-7_19
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DOI: https://doi.org/10.1007/978-3-319-13881-7_19
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