Branching Processes with Immigration and Integer-valued Time Series

Dion, J., Gauthier, G., and Latour, A.. "Branching Processes with Immigration and Integer-valued Time Series." Serdica Mathematical Journal 21.2 (1995): 123-136. <http://eudml.org/doc/11662>.

@article{Dion1995,
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.},
author = {Dion, J., Gauthier, G., Latour, A.},
journal = {Serdica Mathematical Journal},
keywords = {Integer-Valued Time Series; Branching Processes with Immigration; Estimation; Consistency; Asymptotic Normality; GINAR(d); integer-valued autoregressive time series; functionals of multitype branching processes with immigration; existence of a stationary distribution; consistency; asymptotic normality; autoregressive moving average time series},
language = {eng},
number = {2},
pages = {123-136},
publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},
title = {Branching Processes with Immigration and Integer-valued Time Series},
url = {http://eudml.org/doc/11662},
volume = {21},
year = {1995},
}

TY - JOUR
AU - Dion, J.
AU - Gauthier, G.
AU - Latour, A.
TI - Branching Processes with Immigration and Integer-valued Time Series
JO - Serdica Mathematical Journal
PY - 1995
PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences
VL - 21
IS - 2
SP - 123
EP - 136
AB - 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.
LA - eng
KW - Integer-Valued Time Series; Branching Processes with Immigration; Estimation; Consistency; Asymptotic Normality; GINAR(d); integer-valued autoregressive time series; functionals of multitype branching processes with immigration; existence of a stationary distribution; consistency; asymptotic normality; autoregressive moving average time series
UR - http://eudml.org/doc/11662
ER -