Integer-Valued Time Series Branching Processes with Immigration Estimation Consistency 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.