Please use this identifier to cite or link to this item: http://hdl.handle.net/10525/633

 Title: Branching Processes with Immigration and Integer-valued Time Series Authors: Dion, J.Gauthier, G.Latour, A. Keywords: Integer-Valued Time SeriesBranching Processes with ImmigrationEstimationConsistencyAsymptotic 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. URI: http://hdl.handle.net/10525/633 ISSN: 1310-6600 Appears in Collections: Volume 21 Number 2

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