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Title: Branching Processes with Immigration and Integer-valued Time Series
Authors: Dion, J.
Gauthier, G.
Latour, A.
Keywords: Integer-Valued Time Series
Branching Processes with Immigration
Asymptotic Normality
Issue Date: 1995
Publisher: Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Citation: Serdica Mathematical Journal, Vol. 21, No 2, (1995), 123p-136p
Abstract: In this paper, we indicate how integer-valued autoregressive time series Ginar(d) of ordre d, d ≥ 1, are simple functionals of multitype branching processes with immigration. This allows the derivation of a simple criteria for the existence of a stationary distribution of the time series, thus proving and extending some results by Al-Osh and Alzaid [1], Du and Li [9] and Gauthier and Latour [11]. One can then transfer results on estimation in subcritical multitype branching processes to stationary Ginar(d) and get consistency and asymptotic normality for the corresponding estimators. The technique covers autoregressive moving average time series as well.
ISSN: 1310-6600
Appears in Collections:Volume 21 Number 2

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